Matlab Code

Matlab Code

1 %% I m p o r t a n t n o t e s :

2 % To run t h i s s c r i p t you need t h e d a t a s e t ” Spot+DecFutures . x l s x ” .

3 % The c o d e must be run s e c t i o n w i s e , a s s t r u c t u r e d h e r e .

4 % Some o f t h e s u b s e c t i o n s must be runned s e p a r a t e l y , s u c h a s p l o t s and

5 % f i g u r e s .

6 % I f you have any i s s u e s w i t h r u n n i n g t h e s c r i p t , p l e a s e c o n t a c t

7 % s a n d e r . l i e @ s t u d e n t . b i . no

8

9 %% Part 1 − P r e l i m i n a r y a n a l y s i s :

10 % R i s k Premium s t a t i s t i c s

11 c l e a r;

12 c l c;

13

14 % Import d a t a and c r e a t e v a r i a b l e s :

15 d a t a = r e a d t a b l e (’ Spot+DecFutures . x l s x ’) ;

16 d a t a=d a t a ( ˜any( i s m i s s i n g ( d a t a . Spot ) , 2 ) , : ) ;

17 d a t a ( 5 8 4 : 5 8 5 , : ) = [ ] ;

18 d a t a = t a b l e 2 t i m e t a b l e ( d a t a ) ;

19 d a t a . RP19 = d a t a . Fut19 − d a t a . Spot ;

20 d a t a . RP18 = d a t a . Fut18 − d a t a . Spot ;

21 d a t a . RP17 = d a t a . Fut17 − d a t a . Spot ;

22 d a t a . RP16 = d a t a . Fut16 − d a t a . Spot ;

23 d a t a . RP15 = d a t a . Fut15 − d a t a . Spot ;

24 d a t a . RP14 = d a t a . Fut14 − d a t a . Spot ;

25 d a t a ( 1 7 0 0 :end, : ) = [ ] ;

26

27 % S t a t i s t i c s :

28 R e s u l t s = t a b l e ( ) ;

29 R e s u l t s . O b s e r v a t i o n s ( 1 ) = 1 6 9 9 ;

30 R e s u l t s . O b s e r v a t i o n s ( 2 ) = 1 4 5 4 ;

31 R e s u l t s . O b s e r v a t i o n s ( 3 ) = 1 2 0 7 ;

32 R e s u l t s . O b s e r v a t i o n s ( 4 ) = 9 8 3 ;

33 R e s u l t s . O b s e r v a t i o n s ( 5 ) = 7 2 9 ;

34 R e s u l t s . O b s e r v a t i o n s ( 6 ) = 4 8 5 ;

35

36 R e s u l t s . Mean ( 1 ) = mean( d a t a . RP19 ( 1 : 1 6 9 9 ) ) ;

37 R e s u l t s . Mean ( 2 ) = mean( d a t a . RP18 ( 1 : 1 4 5 4 ) ) ;

38 R e s u l t s . Mean ( 3 ) = mean( d a t a . RP17 ( 1 : 1 2 0 7 ) ) ;

39 R e s u l t s . Mean ( 4 ) = mean( d a t a . RP16 ( 1 : 9 8 3 ) ) ;

40 R e s u l t s . Mean ( 5 ) = mean( d a t a . RP15 ( 1 : 7 2 9 ) ) ;

41 R e s u l t s . Mean ( 6 ) = mean( d a t a . RP14 ( 1 : 4 8 5 ) ) ;

42

43 R e s u l t s . Std ( 1 ) = s t d( d a t a . RP19 ( 1 : 1 6 9 9 ) ) ;

44 R e s u l t s . Std ( 2 ) = s t d( d a t a . RP18 ( 1 : 1 4 5 4 ) ) ;

45 R e s u l t s . Std ( 3 ) = s t d( d a t a . RP17 ( 1 : 1 2 0 7 ) ) ;

46 R e s u l t s . Std ( 4 ) = s t d( d a t a . RP16 ( 1 : 9 8 3 ) ) ;

47 R e s u l t s . Std ( 5 ) = s t d( d a t a . RP15 ( 1 : 7 2 9 ) ) ;

48 R e s u l t s . Std ( 6 ) = s t d( d a t a . RP14 ( 1 : 4 8 5 ) ) ;

49

50 R e s u l t s . Skew ( 1 ) = s k e w n e s s ( d a t a . RP19 ( 1 : 1 6 9 9 ) ) ;

51 R e s u l t s . Skew ( 2 ) = s k e w n e s s ( d a t a . RP18 ( 1 : 1 4 5 4 ) ) ;

52 R e s u l t s . Skew ( 3 ) = s k e w n e s s ( d a t a . RP17 ( 1 : 1 2 0 7 ) ) ;

53 R e s u l t s . Skew ( 4 ) = s k e w n e s s ( d a t a . RP16 ( 1 : 9 8 3 ) ) ;

54 R e s u l t s . Skew ( 5 ) = s k e w n e s s ( d a t a . RP15 ( 1 : 7 2 9 ) ) ;

55 R e s u l t s . Skew ( 6 ) = s k e w n e s s ( d a t a . RP14 ( 1 : 4 8 5 ) ) ;

56

57 R e s u l t s . ExKurt ( 1 ) = k u r t o s i s ( d a t a . RP19 ( 1 : 1 6 9 9 ) )−3;

58 R e s u l t s . ExKurt ( 2 ) = k u r t o s i s ( d a t a . RP18 ( 1 : 1 4 5 4 ) )−3;

59 R e s u l t s . ExKurt ( 3 ) = k u r t o s i s ( d a t a . RP17 ( 1 : 1 2 0 7 ) )−3;

60 R e s u l t s . ExKurt ( 4 ) = k u r t o s i s ( d a t a . RP16 ( 1 : 9 8 3 ) )−3;

61 R e s u l t s . ExKurt ( 5 ) = k u r t o s i s ( d a t a . RP15 ( 1 : 7 2 9 ) )−3;

62 R e s u l t s . ExKurt ( 6 ) = k u r t o s i s ( d a t a . RP14 ( 1 : 4 8 5 ) )−3;

63

64 f i g u r e;

65 p l o t( d a t a . Date , d a t a . RP19 )

66 h o l d on

67 p l o t( d a t a . Date , d a t a . RP18 )

68 p l o t( d a t a . Date , d a t a . RP17 )

69 p l o t( d a t a . Date , d a t a . RP16 )

70 p l o t( d a t a . Date , d a t a . RP15 )

71 p l o t( d a t a . Date , d a t a . RP14 )

72 h o l d o f f

73 l e g e n d(’RP 19 ’, ’RP 18 ’, ’RP 17 ’, ’RP 16 ’, ’RP 15 ’, ’RP 14 ’)

74 box (’ o f f ’)

75 x l a b e l(’ Year ’) ;

76 y l a b e l(’ R i s k Premium i n EUR ’)

77

78 % H i s t o r i c a l p r i c e s o f e m i s s i o n a l l o w a n c e s

79 f i g u r e;

80 p l o t( d a t a . Date , d a t a . Spot )

81 h o l d on

82 p l o t( d a t a . Date , d a t a . Fut19 ) ;

83 p l o t( d a t a . Date , d a t a . Fut18 ) ;

84 p l o t( d a t a . Date , d a t a . Fut17 ) ;

85 p l o t( d a t a . Date , d a t a . Fut16 ) ;

86 p l o t( d a t a . Date , d a t a . Fut15 ) ;

87 p l o t( d a t a . Date , d a t a . Fut14 ) ;

88 l e g e n d(’ Spot ’, ’ Fut19 ’, ’ Fut18 ’, ’ Fut17 ’, ’ Fut16 ’, ’ Fut15 ’, ’ Fut14 ’, ’ L o c a t i o n ’ , ’ SouthEast ’)

89 x l a b e l(’ Year ’) ;

90 y l a b e l(’ P r i c e ( i n EUR) ’) ;

91 h o l d o f f

92

93 %% Part 2 − ADF t e s t s

94 c l e a r;

95 c l c;

96

97 % Import d a t a

98 d a t a = r e a d t a b l e (’ Spot+DecFutures . x l s x ’) ;

99 d a t a=d a t a ( ˜any( i s m i s s i n g ( d a t a . Spot ) , 2 ) , : ) ;

100 d a t a ( 5 8 4 : 5 8 5 , : ) = [ ] ;

101 d a t a = t a b l e 2 t i m e t a b l e ( d a t a ) ;

102

103 %C r e a t i n g l o g s :

104 d a t a . Spot = l o g( d a t a . Spot ) ;

105 d a t a . Fut19 = l o g( d a t a . Fut19 ) ;

106 d a t a . Fut18 = l o g( d a t a . Fut18 ) ;

107 d a t a . Fut17 = l o g( d a t a . Fut17 ) ;

108 d a t a . Fut16 = l o g( d a t a . Fut16 ) ;

109 d a t a . Fut15 = l o g( d a t a . Fut15 ) ;

110 d a t a . Fut14 = l o g( d a t a . Fut14 ) ;

111 d a t a . E l e c t r i c i t y = l o g( d a t a . E l e c t r i c i t y ) ;

112 d a t a . E l e c = d a t a . E l e c t r i c i t y ;

113 d a t a . Coal = l o g( d a t a . Coal ) ;

114 d a t a .DAX = l o g( d a t a .DAX) ;

115 d a t a . NaturalGAS = l o g( d a t a . NaturalGAS ) ;

116 d a t a . Ngas = d a t a . NaturalGAS ;

117

118 % C r e a t e a t i m e s e r i e s c o n t a i n i n g f i r s t d i f f e r e n c e s

119 d a t a . S p o t f i r s t d i f f = d a t a . Spot − l a g m a t r i x ( d a t a . Spot , 1 ) ;

120 d a t a . F u t 1 9 f i r s t d i f f = d a t a . Fut19 − l a g m a t r i x ( d a t a . Fut19 , 1 ) ;

121 d a t a . F u t 1 8 f i r s t d i f f = d a t a . Fut18 − l a g m a t r i x ( d a t a . Fut18 , 1 ) ;

122 d a t a . F u t 1 7 f i r s t d i f f = d a t a . Fut17 − l a g m a t r i x ( d a t a . Fut17 , 1 ) ;

123 d a t a . F u t 1 6 f i r s t d i f f = d a t a . Fut16 − l a g m a t r i x ( d a t a . Fut16 , 1 ) ;

124 d a t a . F u t 1 5 f i r s t d i f f = d a t a . Fut15 − l a g m a t r i x ( d a t a . Fut15 , 1 ) ;

125 d a t a . F u t 1 4 f i r s t d i f f = d a t a . Fut14 − l a g m a t r i x ( d a t a . Fut14 , 1 ) ;

126 d a t a . O i l f d = d a t a . O i l − l a g m a t r i x ( d a t a . O i l , 1 ) ;

127 d a t a . E l e c f d = d a t a . E l e c − l a g m a t r i x ( d a t a . E l e c , 1 ) ;

128 d a t a . C o a l f d = d a t a . Coal − l a g m a t r i x ( d a t a . Coal , 1 ) ;

129 d a t a . DAX fd = d a t a .DAX− l a g m a t r i x ( d a t a .DAX, 1 ) ;

130 d a t a . N g a s f d = d a t a . Ngas − l a g m a t r i x ( d a t a . Ngas , 1 ) ;

131

132 % ADF T e s t ( Unit r o o t t e s t ) − Check e a c h t i m e s e r i e s f o r s t a t i o n a r i t y

133 r e s u l t s = t a b l e ( ) ;

134

135 i = 0 : 2 ;

136 f o r model = i

137 maxlag = 1 2 ;

138 i c = ’ AIC ’;

139 a l p h a = [ 0 . 0 1 ; 0 . 0 5 ; 0 . 1 0 ] ;

140 model

141 142

143 % Spot :

144

145 % L e v e l s

146 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Spot , model , maxlag , i c ) ;

147 d i s p(’ Spot L e v e l s ’) ;

148 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

149 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

150 r e j e c t = a d f s t a t > c r i t v a l ;

151 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

152 i f model == 0

153 r e s u l t s . S p o t L e v e l s ( 1 ) = a d f s t a t ;

154 end

155 i f model == 1

156 r e s u l t s . S p o t L e v e l s ( 2 ) = a d f s t a t ;

157 end

158 i f model == 2

159 r e s u l t s . S p o t L e v e l s ( 3 ) = a d f s t a t ;

160 end

161 162

163 % F i r s t d i f f e r e n c e s

164 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . S p o t f i r s t d i f f ( 2 :end) , model , maxlag , i c ) ;

165 d i s p(’ Spot f i r s t d i f f e r e n c e s ’) ;

166 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

167 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

168 r e j e c t = a d f s t a t > c r i t v a l ;

169 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

170 i f model == 0

171 r e s u l t s . S p o t D i f f ( 1 ) = a d f s t a t ;

172 end

173 i f model == 1

174 r e s u l t s . S p o t D i f f ( 2 ) = a d f s t a t ;

175 end

176 i f model == 2

177 r e s u l t s . S p o t D i f f ( 3 ) = a d f s t a t ;

178 end

179

180 % Dec2019 Future

181 % L e v e l s

182 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut19 ( 1 : 1 6 9 9 ) , model , maxlag , i c ) ;

183 d i s p(’ Fut19 L e v e l s ’) ;

184 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

185 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

186 r e j e c t = a d f s t a t > c r i t v a l ;

187 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

188 i f model == 0

189 r e s u l t s . F u t 1 9 L e v e l s ( 1 ) = a d f s t a t ;

190 end

191 i f model == 1

192 r e s u l t s . F u t 1 9 L e v e l s ( 2 ) = a d f s t a t ;

193 end

194 i f model == 2

195 r e s u l t s . F u t 1 9 L e v e l s ( 3 ) = a d f s t a t ;

196 end

197

198 % F i r s t d i f f e r e n c e s

199 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 9 f i r s t d i f f ( 2 : 1 6 9 9 ) , model , maxlag , i c ) ;

200 d i s p(’ Fut19 f i r s t d i f f e r e n c e s ’) ;

201 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

202 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

203 r e j e c t = a d f s t a t > c r i t v a l ;

204 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

205 i f model == 0

206 r e s u l t s . F u t 1 9 D i f f ( 1 ) = a d f s t a t ;

207 end

208 i f model == 1

209 r e s u l t s . F u t 1 9 D i f f ( 2 ) = a d f s t a t ;

210 end

211 i f model == 2

212 r e s u l t s . F u t 1 9 D i f f ( 3 ) = a d f s t a t ;

213 end

214 215

216 % Dec2018 Future

217 % L e v e l s

218 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut18 ( 1 : 1 4 5 4 ) , model , maxlag , i c ) ;

219 d i s p(’ Fut18 L e v e l s ’) ;

220 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

221 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

222 r e j e c t = a d f s t a t > c r i t v a l ;

223 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

224 i f model == 0

225 r e s u l t s . F u t 1 8 L e v e l s ( 1 ) = a d f s t a t ;

226 end

227 i f model == 1

228 r e s u l t s . F u t 1 8 L e v e l s ( 2 ) = a d f s t a t ;

229 end

230 i f model == 2

231 r e s u l t s . F u t 1 8 L e v e l s ( 3 ) = a d f s t a t ;

232 end

233

234 % F i r s t d i f f e r e n c e s

235 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 8 f i r s t d i f f ( 2 : 1 4 5 4 ) , model , maxlag , i c ) ;

236 d i s p(’ Fut18 f i r s t d i f f e r e n c e s ’) ;

237 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

238 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

239 r e j e c t = a d f s t a t > c r i t v a l ;

240 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

241 i f model == 0

242 r e s u l t s . F u t 1 8 D i f f ( 1 ) = a d f s t a t ;

243 end

244 i f model == 1

245 r e s u l t s . F u t 1 8 D i f f ( 2 ) = a d f s t a t ;

246 end

247 i f model == 2

248 r e s u l t s . F u t 1 8 D i f f ( 3 ) = a d f s t a t ;

249 end

250 251

252 % Dec2017 Future

253 % L e v e l s

254 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut17 ( 1 : 1 2 0 7 ) , model , maxlag , i c ) ;

255 d i s p(’ Fut17 L e v e l s ’) ;

256 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

257 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

258 r e j e c t = a d f s t a t > c r i t v a l ;

259 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

260 i f model == 0

261 r e s u l t s . F u t 1 7 L e v e l s ( 1 ) = a d f s t a t ;

262 end

263 i f model == 1

264 r e s u l t s . F u t 1 7 L e v e l s ( 2 ) = a d f s t a t ;

265 end

266 i f model == 2

267 r e s u l t s . F u t 1 7 L e v e l s ( 3 ) = a d f s t a t ;

268 end

269

270 % F i r s t d i f f e r e n c e s

271 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 7 f i r s t d i f f ( 2 : 1 2 0 7 ) , model , maxlag , i c ) ;

272 d i s p(’ Fut17 f i r s t d i f f e r e n c e s ’) ;

273 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

274 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

275 r e j e c t = a d f s t a t > c r i t v a l ;

276 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

277 i f model == 0

278 r e s u l t s . F u t 1 7 D i f f ( 1 ) = a d f s t a t ;

279 end

280 i f model == 1

281 r e s u l t s . F u t 1 7 D i f f ( 2 ) = a d f s t a t ;

282 end

283 i f model == 2

284 r e s u l t s . F u t 1 7 D i f f ( 3 ) = a d f s t a t ;

285 end

286 287

288 % Dec2016 Future

289 % L e v e l s

290 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut16 ( 1 : 9 8 3 ) , model , maxlag , i c ) ;

291 d i s p(’ Fut16 L e v e l s ’) ;

292 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

293 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

294 r e j e c t = a d f s t a t > c r i t v a l ;

295 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

296 i f model == 0

297 r e s u l t s . F u t 1 6 L e v e l s ( 1 ) = a d f s t a t ;

298 end

299 i f model == 1

300 r e s u l t s . F u t 1 6 L e v e l s ( 2 ) = a d f s t a t ;

301 end

302 i f model == 2

303 r e s u l t s . F u t 1 6 L e v e l s ( 3 ) = a d f s t a t ;

304 end

305

306 % F i r s t d i f f e r e n c e s

307 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 6 f i r s t d i f f ( 2 : 9 8 3 ) , model , maxlag , i c ) ;

308 d i s p(’ Fut16 f i r s t d i f f e r e n c e s ’) ;

309 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

310 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

311 r e j e c t = a d f s t a t > c r i t v a l ;

312 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

313 i f model == 0

314 r e s u l t s . F u t 1 6 D i f f ( 1 ) = a d f s t a t ;

315 end

316 i f model == 1

317 r e s u l t s . F u t 1 6 D i f f ( 2 ) = a d f s t a t ;

318 end

319 i f model == 2

320 r e s u l t s . F u t 1 6 D i f f ( 3 ) = a d f s t a t ;

321 end

322

323 % Dec2015 Future

324 % L e v e l s

325 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut15 ( 1 : 7 2 9 ) , model , maxlag , i c ) ;

326 d i s p(’ Fut15 L e v e l s ’) ;

327 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

328 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

329 r e j e c t = a d f s t a t > c r i t v a l ;

330 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

331 i f model == 0

332 r e s u l t s . F u t 1 5 L e v e l s ( 1 ) = a d f s t a t ;

333 end

334 i f model == 1

335 r e s u l t s . F u t 1 5 L e v e l s ( 2 ) = a d f s t a t ;

336 end

337 i f model == 2

338 r e s u l t s . F u t 1 5 L e v e l s ( 3 ) = a d f s t a t ;

339 end

340

341 % F i r s t d i f f e r e n c e s

342 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 5 f i r s t d i f f ( 2 : 7 2 9 ) , model , maxlag , i c ) ;

343 d i s p(’ Fut15 f i r s t d i f f e r e n c e s ’) ;

344 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

345 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

346 r e j e c t = a d f s t a t > c r i t v a l ;

347 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

348 i f model == 0

349 r e s u l t s . F u t 1 5 D i f f ( 1 ) = a d f s t a t ;

350 end

351 i f model == 1

352 r e s u l t s . F u t 1 5 D i f f ( 2 ) = a d f s t a t ;

353 end

354 i f model == 2

355 r e s u l t s . F u t 1 5 D i f f ( 3 ) = a d f s t a t ;

356 end

357

358 % Dec2014 Future

359 % L e v e l s

360 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Fut14 ( 1 : 4 8 5 ) , model , maxlag , i c ) ;

361 d i s p(’ Fut14 L e v e l s ’) ;

362 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

363 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

364 r e j e c t = a d f s t a t > c r i t v a l ;

365 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

366 i f model == 0

367 r e s u l t s . F u t 1 4 L e v e l s ( 1 ) = a d f s t a t ;

368 end

369 i f model == 1

370 r e s u l t s . F u t 1 4 L e v e l s ( 2 ) = a d f s t a t ;

371 end

372 i f model == 2

373 r e s u l t s . F u t 1 4 L e v e l s ( 3 ) = a d f s t a t ;

374 end

375

376 % F i r s t d i f f e r e n c e s

377 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . F u t 1 4 f i r s t d i f f ( 2 : 4 8 5 ) , model , maxlag , i c ) ;

378 d i s p(’ Fut14 f i r s t d i f f e r e n c e s ’) ;

379 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

380 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

381 r e j e c t = a d f s t a t > c r i t v a l ;

382 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

383 i f model == 0

384 r e s u l t s . F u t 1 4 D i f f ( 1 ) = a d f s t a t ;

385 end

386 i f model == 1

387 r e s u l t s . F u t 1 4 D i f f ( 2 ) = a d f s t a t ;

388 end

389 i f model == 2

390 r e s u l t s . F u t 1 4 D i f f ( 3 ) = a d f s t a t ;

391 end

392

393 % O i l :

394 % L e v e l s

395 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . O i l , model , maxlag , i c ) ;

396 d i s p(’ O i l L e v e l s ’) ;

397 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

398 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

399 r e j e c t = a d f s t a t > c r i t v a l ;

400 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

401 i f model == 0

402 r e s u l t s . O i l L e v e l s ( 1 ) = a d f s t a t ;

403 end

404 i f model == 1

405 r e s u l t s . O i l L e v e l s ( 2 ) = a d f s t a t ;

406 end

407 i f model == 2

408 r e s u l t s . O i l L e v e l s ( 3 ) = a d f s t a t ;

409 end

410 411

412 % F i r s t d i f f e r e n c e s

413 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . O i l f d ( 2 :end) , model , maxlag , i c ) ;

414 d i s p(’ O i l f i r s t d i f f e r e n c e s ’) ;

415 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

416 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

417 r e j e c t = a d f s t a t > c r i t v a l ;

418 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

419 i f model == 0

420 r e s u l t s . O i l D i f f ( 1 ) = a d f s t a t ;

421 end

422 i f model == 1

423 r e s u l t s . O i l D i f f ( 2 ) = a d f s t a t ;

424 end

425 i f model == 2

426 r e s u l t s . O i l D i f f ( 3 ) = a d f s t a t ;

427 end

428

429 % E l e c :

430 % L e v e l s

431 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . E l e c , model , maxlag , i c ) ;

432 d i s p(’ E l e c L e v e l s ’) ;

433 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

434 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

435 r e j e c t = a d f s t a t > c r i t v a l ;

436 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

437 i f model == 0

438 r e s u l t s . E l e c L e v e l s ( 1 ) = a d f s t a t ;

439 end

440 i f model == 1

441 r e s u l t s . E l e c L e v e l s ( 2 ) = a d f s t a t ;

442 end

443 i f model == 2

444 r e s u l t s . E l e c L e v e l s ( 3 ) = a d f s t a t ;

445 end

446

447 % F i r s t d i f f e r e n c e s

448 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . E l e c f d ( 2 :end) , model , maxlag , i c ) ;

449 d i s p(’ E l e c f i r s t d i f f e r e n c e s ’) ;

450 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

451 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

452 r e j e c t = a d f s t a t > c r i t v a l ;

453 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

454 i f model == 0

455 r e s u l t s . E l e c D i f f ( 1 ) = a d f s t a t ;

456 end

457 i f model == 1

458 r e s u l t s . E l e c D i f f ( 2 ) = a d f s t a t ;

459 end

460 i f model == 2

461 r e s u l t s . E l e c D i f f ( 3 ) = a d f s t a t ;

462 end

463 464

465 % Coal :

466 % L e v e l s

467 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( d a t a . Coal ( 5 5 7 :

end) , model , maxlag , i c ) ;

468 d i s p(’ Coal L e v e l s ’) ;

469 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

470 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

471 r e j e c t = a d f s t a t > c r i t v a l ;

472 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

473 i f model == 0

474 r e s u l t s . C o a l L e v e l s ( 1 ) = a d f s t a t ;

475 end

476 i f model == 1

477 r e s u l t s . C o a l L e v e l s ( 2 ) = a d f s t a t ;

478 end

479 i f model == 2

480 r e s u l t s . C o a l L e v e l s ( 3 ) = a d f s t a t ;

481 end

482

483 % F i r s t d i f f e r e n c e s

484 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( d a t a . C o a l f d ( 5 5 8 :end) , model , maxlag , i c ) ;

485 d i s p(’ Coal f i r s t d i f f e r e n c e s ’) ;

486 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

487 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

488 r e j e c t = a d f s t a t > c r i t v a l ;

489 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

490 i f model == 0

491 r e s u l t s . C o a l D i f f ( 1 ) = a d f s t a t ;

492 end

493 i f model == 1

494 r e s u l t s . C o a l D i f f ( 2 ) = a d f s t a t ;

495 end

496 i f model == 2

497 r e s u l t s . C o a l D i f f ( 3 ) = a d f s t a t ;

498 end

499

500 % DAX:

501 % DAX d a t a :

502 DAXdata = t a b l e ( ) ;

503 DAXdata .DAX = d a t a .DAX;

504 DAXdata . DAX fd = d a t a . DAX fd ;

505 DAXdata=DAXdata ( ˜any( i s m i s s i n g ( DAXdata .DAX) , 2 ) , : ) ;

506 DAXdata=DAXdata ( ˜any( i s m i s s i n g ( DAXdata . DAX fd ) , 2 ) , : ) ;

507

508 % L e v e l s

509 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( DAXdata .DAX( 1 : end) , model , maxlag , i c ) ;

510 d i s p(’DAX L e v e l s ’) ;

511 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

512 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

513 r e j e c t = a d f s t a t > c r i t v a l ;

514 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

515 i f model == 0

516 r e s u l t s . DAXLevels ( 1 ) = a d f s t a t ;

517 end

518 i f model == 1

519 r e s u l t s . DAXLevels ( 2 ) = a d f s t a t ;

520 end

521 i f model == 2

522 r e s u l t s . DAXLevels ( 3 ) = a d f s t a t ;

523 end

524

525 % F i r s t d i f f e r e n c e s

526 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( DAXdata . DAX fd ( 1 :end) , model , maxlag , i c ) ;

527 d i s p(’DAX f i r s t d i f f e r e n c e s ’) ;

528 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

529 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

530 r e j e c t = a d f s t a t > c r i t v a l ;

531 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

532 i f model == 0

533 r e s u l t s . DAXDiff ( 1 ) = a d f s t a t ;

534 end

535 i f model == 1

536 r e s u l t s . DAXDiff ( 2 ) = a d f s t a t ;

537 end

538 i f model == 2

539 r e s u l t s . DAXDiff ( 3 ) = a d f s t a t ;

540 end

541

542 % Ngas :

543 % Ngas d a t a :

544 Ngasdata = t a b l e ( ) ;

545 Ngasdata . Ngas = d a t a . Ngas ;

546 Ngasdata . N g a s f d = d a t a . N g a s f d ;

547 Ngasdata=Ngasdata ( ˜any( i s m i s s i n g ( Ngasdata . Ngas ) , 2 ) , : ) ;

548 Ngasdata=Ngasdata ( ˜any( i s m i s s i n g ( Ngasdata . N g a s f d ) , 2 ) , : ) ;

549

550 % L e v e l s

551 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s l e v e l ] = a u g d f a u t o l a g ( Ngasdata . Ngas ( 1 :end) , model , maxlag , i c ) ;

552 d i s p(’ Ngas L e v e l s ’) ;

553 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s l e v e l ) ) ;

554 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

555 r e j e c t = a d f s t a t > c r i t v a l ;

556 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

557 i f model == 0

558 r e s u l t s . N g a s L e v e l s ( 1 ) = a d f s t a t ;

559 end

560 i f model == 1

561 r e s u l t s . N g a s L e v e l s ( 2 ) = a d f s t a t ;

562 end

563 i f model == 2

564 r e s u l t s . N g a s L e v e l s ( 3 ) = a d f s t a t ;

565 end

566

567 % F i r s t d i f f e r e n c e s

568 [ a d f s t a t , p v a l , c r i t v a l , ˜ , l a g s f i r s t d i f f ] = a u g d f a u t o l a g ( Ngasdata . N g a s f d ( 1 :end) , model , maxlag , i c ) ;

569 d i s p(’ Ngas f i r s t d i f f e r e n c e s ’) ;

570 d i s p( t a b l e ( p v a l , a d f s t a t , l a g s f i r s t d i f f ) ) ;

571 c r i t v a l = c r i t v a l ( 1 : 3 ) ;

572 r e j e c t = a d f s t a t > c r i t v a l ;

573 d i s p( t a b l e ( alpha , c r i t v a l , r e j e c t ) ) ;

574 i f model == 0

575 r e s u l t s . N g a s D i f f ( 1 ) = a d f s t a t ;

576 end

577 i f model == 1

578 r e s u l t s . N g a s D i f f ( 2 ) = a d f s t a t ;

579 end

580 i f model == 2

581 r e s u l t s . N g a s D i f f ( 3 ) = a d f s t a t ;

582 end

583 end

584 %% Part 3 − C o i n t e g r a t i o n ( Johansen t e s t ) :

585 c l e a r;

586 c l c;

587

588 % Import d a t a and c r e a t e v a r i a b l e s :

589 d a t a = r e a d t a b l e (’ Spot+DecFutures . x l s x ’) ;

590 d a t a=d a t a ( ˜any( i s m i s s i n g ( d a t a . Spot ) , 2 ) , : ) ;

591 d a t a ( 5 8 4 : 5 8 5 , : ) = [ ] ;

592 d a t a = t a b l e 2 t i m e t a b l e ( d a t a ) ;

593 d a t a . Spot = l o g( d a t a . Spot ) ;

594 d a t a . Fut19 = l o g( d a t a . Fut19 ) ;

595 d a t a . Fut18 = l o g( d a t a . Fut18 ) ;

596 d a t a . Fut17 = l o g( d a t a . Fut17 ) ;

597 d a t a . Fut16 = l o g( d a t a . Fut16 ) ;

598 d a t a . Fut15 = l o g( d a t a . Fut15 ) ;

599 d a t a . Fut14 = l o g( d a t a . Fut14 ) ;

600

601 % D e t e r m i n i n g l a g l e v e l s :

602 % Spot and Fut19 :

603 r e g 1 = t a b l e ( ) ;

604 r e g 1 . Spot = d a t a . Spot ;

605 r e g 1 . Fut19 = d a t a . Fut19 ;

606 r e g 1 ( 1 7 0 0 :end, : ) = [ ] ;

607 r e g 1 = r e g 1{: , :};

608 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 1 , 1 2 )

609 %Optimal = 12

610

611 % Spot and Fut18 :

612 r e g 2 = t a b l e ( ) ;

613 r e g 2 . Spot = d a t a . Spot ;

614 r e g 2 . Fut18 = d a t a . Fut18 ;

615 r e g 2 ( 1 4 5 5 :end, : ) = [ ] ;

616 r e g 2 = r e g 2{: , :};

617 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 2 , 1 2 )

618 %Optimal = 8

619

620 % Spot and Fut17 :

621 r e g 3 = t a b l e ( ) ;

622 r e g 3 . Spot = d a t a . Spot ;

623 r e g 3 . Fut17 = d a t a . Fut17 ;

624 r e g 3 ( 1 2 0 8 :end, : ) = [ ] ;

625 r e g 3 = r e g 3{: , :};

626 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 3 , 1 2 )

627 %Optimal = 12

628

629 %Spot and Fut16

630 r e g 4 = t a b l e ( ) ;

631 r e g 4 . Spot = d a t a . Spot ;

632 r e g 4 . Fut16 = d a t a . Fut16 ;

633 r e g 4 ( 9 8 4 :end, : ) = [ ] ;

634 r e g 4 = r e g 4{: , :};

635 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 4 , 1 2 )

636 %Optimal = 7

637

638 % Spot and Fut15

639 r e g 5 = t a b l e ( ) ;

640 r e g 5 . Spot = d a t a . Spot ;

641 r e g 5 . Fut15 = d a t a . Fut15 ;

642 r e g 5 ( 7 3 0 :end, : ) = [ ] ;

643 r e g 5 = r e g 5{: , :};

644 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 5 , 1 2 )

645 %Optimal = 10

646

647 %Spot and Fut14

648 r e g 6 = t a b l e ( ) ;

649 r e g 6 . Spot = d a t a . Spot ;

650 r e g 6 . Fut14 = d a t a . Fut14 ;

651 r e g 6 ( 4 8 6 :end, : ) = [ ] ;

652 r e g 6 = r e g 6{: , :};

653 [ l a g l e n g t h , AIC , l o g L ] = VARlag ( r e g 6 , 1 2 )

654 %Optimal = 7

655

656 %T a b l e s f o r r e s u l t s :

657 t r a c e H 0 = t a b l e ( ) ;

658 MaxEigH0 = t a b l e ( ) ;

659 t r a c e H 1 = t a b l e ( ) ;

660 MaxEigH1 = t a b l e ( ) ;

661

662 % Spot and Fut19 :

663 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

664 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 1 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ t r a c e ’, ’ d i s p l a y ’, ’ o f f ’) ;

665 d i s p(’ t r a c e H0 ’) ;

666 d i s p( pValue ) ;

667 t r a c e H 0 . Fut19 ( 1 ) = pValue . r 0 ;

668 t r a c e H 0 . Fut19 ( 2 ) = pValue . r 1 ;

669

670 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 1 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

671 d i s p(’ max e i g e n v e c t o r H0 ’) ;

672 d i s p( pValue ) ;

673 MaxEigH0 . Fut19 ( 1 ) = pValue . r 0 ;

674 MaxEigH0 . Fut19 ( 2 ) = pValue . r 1 ;

675

676 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

677 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 1 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

678 d i s p(’ t r a c e H1 ’) ;

679 d i s p( pValue )

680 t r a c e H 1 . Fut19 ( 1 ) = pValue . r 0 ;

681 t r a c e H 1 . Fut19 ( 2 ) = pValue . r 1 ;

682

683 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 1 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

684 d i s p(’ max e i g e n v e c t o r H1 ’) ;

685 d i s p( pValue ) ;

686 MaxEigH1 . Fut19 ( 1 ) = pValue . r 0 ;

687 MaxEigH1 . Fut19 ( 2 ) = pValue . r 1 ;

688

689 % Spot and Fut18 :

690 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

691 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 2 , ’ model ’, ’ H1∗’,’ l a g s ’, 8 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

692 d i s p(’ t r a c e H0 ’) ;

693 d i s p( pValue ) ;

694 t r a c e H 0 . Fut18 ( 1 ) = pValue . r 0 ;

695 t r a c e H 0 . Fut18 ( 2 ) = pValue . r 1 ;

696

697 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 2 , ’ model ’, ’ H1∗’,’ l a g s ’, 8 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

698 d i s p(’ max e i g e n v e c t o r H0 ’) ;

699 d i s p( pValue ) ;

700 MaxEigH0 . Fut18 ( 1 ) = pValue . r 0 ;

701 MaxEigH0 . Fut18 ( 2 ) = pValue . r 1 ;

702

703 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

704 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 2 , ’ model ’, ’ H2 ’,’ l a g s ’, 8 , ’ t e s t ’, ’ t r a c e ’ , ’ d i s p l a y ’, ’ o f f ’) ;

705 d i s p(’ t r a c e H1 ’) ;

706 d i s p( pValue ) ;

707 t r a c e H 1 . Fut18 ( 1 ) = pValue . r 0 ;

708 t r a c e H 1 . Fut18 ( 2 ) = pValue . r 1 ;

709

710 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 2 , ’ model ’, ’ H2 ’,’ l a g s ’, 8 , ’ t e s t ’, ’ maxeig

’, ’ d i s p l a y ’, ’ o f f ’) ;

711 d i s p(’ max e i g e n v e c t o r H1 ’) ;

712 d i s p( pValue ) ;

713 MaxEigH1 . Fut18 ( 1 ) = pValue . r 0 ;

714 MaxEigH1 . Fut18 ( 2 ) = pValue . r 1 ;

715

716 % Spot and Fut17 :

717 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

718 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 3 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ t r a c e ’, ’ d i s p l a y ’, ’ o f f ’) ;

719 d i s p(’ t r a c e H0 ’) ;

720 d i s p( pValue ) ;

721 t r a c e H 0 . Fut17 ( 1 ) = pValue . r 0 ;

722 t r a c e H 0 . Fut17 ( 2 ) = pValue . r 1 ;

723

724 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 3 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

725 d i s p(’ max e i g e n v e c t o r H0 ’) ;

726 d i s p( pValue ) ;

727 MaxEigH0 . Fut17 ( 1 ) = pValue . r 0 ;

728 MaxEigH0 . Fut17 ( 2 ) = pValue . r 1 ;

729

730 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

731 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 3 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

732 d i s p(’ t r a c e H1 ’) ;

733 d i s p( pValue ) ;

734 t r a c e H 1 . Fut17 ( 1 ) = pValue . r 0 ;

735 t r a c e H 1 . Fut17 ( 2 ) = pValue . r 1 ;

736

737 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 3 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 2 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

738 d i s p(’ max e i g e n v e c t o r H1 ’) ;

739 d i s p( pValue ) ;

740 MaxEigH1 . Fut17 ( 1 ) = pValue . r 0 ;

741 MaxEigH1 . Fut17 ( 2 ) = pValue . r 1 ;

742

743 % Spot and Fut16 :

744 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

745 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 4 , ’ model ’, ’ H1∗’,’ l a g s ’, 7 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

746 d i s p(’ t r a c e H0 ’) ;

747 d i s p( pValue ) ;

748 t r a c e H 0 . Fut16 ( 1 ) = pValue . r 0 ;

749 t r a c e H 0 . Fut16 ( 2 ) = pValue . r 1 ;

750

751 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 4 , ’ model ’, ’ H1∗’,’ l a g s ’, 7 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

752 d i s p(’ max e i g e n v e c t o r H0 ’) ;

753 d i s p( pValue ) ;

754 MaxEigH0 . Fut16 ( 1 ) = pValue . r 0 ;

755 MaxEigH0 . Fut16 ( 2 ) = pValue . r 1 ;

756

757 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

758 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 4 , ’ model ’, ’ H2 ’,’ l a g s ’, 7 , ’ t e s t ’, ’ t r a c e ’ , ’ d i s p l a y ’, ’ o f f ’) ;

759 d i s p(’ t r a c e H1 ’) ;

760 d i s p( pValue ) ;

761 t r a c e H 1 . Fut16 ( 1 ) = pValue . r 0 ;

762 t r a c e H 1 . Fut16 ( 2 ) = pValue . r 1 ;

763

764 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 4 , ’ model ’, ’ H2 ’,’ l a g s ’, 7 , ’ t e s t ’, ’ maxeig

’, ’ d i s p l a y ’, ’ o f f ’) ;

765 d i s p(’ max e i g e n v e c t o r H1 ’) ;

766 d i s p( pValue ) ;

767 MaxEigH1 . Fut16 ( 1 ) = pValue . r 0 ;

768 MaxEigH1 . Fut16 ( 2 ) = pValue . r 1 ;

769

770 % Spot and Fut15 :

771 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

772 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 5 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 0 , ’ t e s t ’, ’ t r a c e ’, ’ d i s p l a y ’, ’ o f f ’) ;

773 d i s p(’ t r a c e H0 ’) ;

774 d i s p( pValue ) ;

775 t r a c e H 0 . Fut15 ( 1 ) = pValue . r 0 ;

776 t r a c e H 0 . Fut15 ( 2 ) = pValue . r 1 ;

777

778 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 5 , ’ model ’, ’ H1∗’,’ l a g s ’, 1 0 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

779 d i s p(’ max e i g e n v e c t o r H0 ’) ;

780 d i s p( pValue ) ;

781 MaxEigH0 . Fut15 ( 1 ) = pValue . r 0 ;

782 MaxEigH0 . Fut15 ( 2 ) = pValue . r 1 ;

783

784 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

785 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 5 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 0 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

786 d i s p(’ t r a c e H1 ’) ;

787 d i s p( pValue ) ;

788 t r a c e H 1 . Fut15 ( 1 ) = pValue . r 0 ;

789 t r a c e H 1 . Fut15 ( 2 ) = pValue . r 1 ;

790

791 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 5 , ’ model ’, ’ H2 ’,’ l a g s ’, 1 0 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

792 d i s p(’ max e i g e n v e c t o r H1 ’) ;

793 d i s p( pValue ) ;

794 MaxEigH1 . Fut15 ( 1 ) = pValue . r 0 ;

795 MaxEigH1 . Fut15 ( 2 ) = pValue . r 1 ;

796

797 % Spot and Fut14 :

798 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h i n t e r c e p t but no t r e n d

799 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 6 , ’ model ’, ’ H1∗’,’ l a g s ’, 7 , ’ t e s t ’, ’ t r a c e

’, ’ d i s p l a y ’, ’ o f f ’) ;

800 d i s p(’ t r a c e H0 ’) ;

801 d i s p( pValue ) ;

802 t r a c e H 0 . Fut14 ( 1 ) = pValue . r 0 ;

803 t r a c e H 0 . Fut14 ( 2 ) = pValue . r 1 ;

804

805 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 6 , ’ model ’, ’ H1∗’,’ l a g s ’, 7 , ’ t e s t ’, ’ maxeig ’, ’ d i s p l a y ’, ’ o f f ’) ;

806 d i s p(’ max e i g e n v e c t o r H0 ’) ;

807 d i s p( pValue ) ;

808 MaxEigH0 . Fut14 ( 1 ) = pValue . r 0 ;

809 MaxEigH0 . Fut14 ( 2 ) = pValue . r 1 ;

810

811 % N u l l h y p o t h e s i s − c o i n t e g r a t e d s e r i e s w i t h no i n t e r c e p t , no t r e n d

812 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 6 , ’ model ’, ’ H2 ’,’ l a g s ’, 7 , ’ t e s t ’, ’ t r a c e ’ , ’ d i s p l a y ’, ’ o f f ’) ;

813 d i s p(’ t r a c e H1 ’) ;

814 d i s p( pValue ) ;

815 t r a c e H 1 . Fut14 ( 1 ) = pValue . r 0 ;

816 t r a c e H 1 . Fut14 ( 2 ) = pValue . r 1 ;

817

818 [ ˜ , pValue , ˜ , ˜ , ˜ ] = j c i t e s t ( r e g 6 , ’ model ’, ’ H2 ’,’ l a g s ’, 7 , ’ t e s t ’, ’ maxeig

’, ’ d i s p l a y ’, ’ o f f ’) ;

819 d i s p(’ max e i g e n v e c t o r H1 ’) ;

820 d i s p( pValue ) ;

821 MaxEigH1 . Fut14 ( 1 ) = pValue . r 0 ;

822 MaxEigH1 . Fut14 ( 2 ) = pValue . r 1 ;

823

824 %% Part 4 −ECM and ECM−GARCH:

825 c l e a r;

826 c l c;

827

828 % Import d a t a and c r e a t e v a r i a b l e s :

829 d a t a = r e a d t a b l e (’ Spot+DecFutures . x l s x ’) ;

830 d a t a=d a t a ( ˜any( i s m i s s i n g ( d a t a . Spot ) , 2 ) , : ) ;

831 d a t a ( 5 8 4 : 5 8 5 , : ) = [ ] ;

832 d a t a = t a b l e 2 t i m e t a b l e ( d a t a ) ;

833 d a t a . Spot = l o g( d a t a . Spot ) ;

834 d a t a . Fut19 = l o g( d a t a . Fut19 ) ;

835 d a t a . Fut18 = l o g( d a t a . Fut18 ) ;

836 d a t a . Fut17 = l o g( d a t a . Fut17 ) ;

837 d a t a . Fut16 = l o g( d a t a . Fut16 ) ;

838 d a t a . Fut15 = l o g( d a t a . Fut15 ) ;

839 d a t a . Fut14 = l o g( d a t a . Fut14 ) ;

840

841 % C r e a t i n g f i r s t d i f f e r e n c e s :

842 d a t a . S p o t f i r s t d i f f = d a t a . Spot − l a g m a t r i x ( d a t a . Spot , 1 ) ;

843 d a t a . F u t 1 9 f i r s t d i f f = d a t a . Fut19 − l a g m a t r i x ( d a t a . Fut19 , 1 ) ;

844 d a t a . F u t 1 8 f i r s t d i f f = d a t a . Fut18 − l a g m a t r i x ( d a t a . Fut18 , 1 ) ;

845 d a t a . F u t 1 7 f i r s t d i f f = d a t a . Fut17 − l a g m a t r i x ( d a t a . Fut17 , 1 ) ;

846 d a t a . F u t 1 6 f i r s t d i f f = d a t a . Fut16 − l a g m a t r i x ( d a t a . Fut16 , 1 ) ;

847 d a t a . F u t 1 5 f i r s t d i f f = d a t a . Fut15 − l a g m a t r i x ( d a t a . Fut15 , 1 ) ;

848 d a t a . F u t 1 4 f i r s t d i f f = d a t a . Fut14 − l a g m a t r i x ( d a t a . Fut14 , 1 ) ;

849

850 % F i n d i n g r e s i d u a l s between Spot and l a g g e d Fut19 :

851 r e g 1 = t a b l e ( ) ;

852 r e g 1 . Date = d a t a . Date ;

853 r e g 1 . Spot = d a t a . Spot ;

854 r e g 1 . LagFut19 = l a g m a t r i x ( d a t a . Fut19 , 1 ) ;

855 r e g 1 ( 1 , : ) = [ ] ;

856 r e g 1 ( 1 7 0 0 :end, : ) = [ ] ;

857 model1 = f i t l m ( r e g 1 , ’ Spot ˜ LagFut19 ’)

858 r e g 1 . r e s i d u a l s 1 = model1 . R e s i d u a l s . Raw ;

859 f i g u r e;

860 p l o t( r e g 1 . Date , r e g 1 . r e s i d u a l s 1 ) ;

861

862 % D e f i n i n g ECM v a r i a b l e s − Spot and Fut19 :

863 ECM1 = t a b l e ( ) ;

864 ECM1. Date = r e g 1 . Date ;

865 ECM1. S p o t f i r s t d i f f = d a t a . S p o t f i r s t d i f f ( 2 : 1 7 0 0 ) ;

866 ECM1. L a g g e d R e s i d u a l s = l a g m a t r i x ( r e g 1 . r e s i d u a l s 1 , 1 ) ;

867 %Lag v a r i a b l e s − Fut :

868 ECM1. F u t 1 9 f i r s t d i f f l a g 1 = r e g 1 . LagFut19 − l a g m a t r i x ( r e g 1 . LagFut19 , 1 ) ;

869 ECM1. F u t 1 9 f i r s t d i f f l a g 2 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 1 ) ;

870 ECM1. F u t 1 9 f i r s t d i f f l a g 3 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 2 ) ;

871 ECM1. F u t 1 9 f i r s t d i f f l a g 4 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 3 ) ;

872 ECM1. F u t 1 9 f i r s t d i f f l a g 5 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 4 ) ;

873 ECM1. F u t 1 9 f i r s t d i f f l a g 6 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 5 ) ;

874 ECM1. F u t 1 9 f i r s t d i f f l a g 7 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 6 ) ;

875 ECM1. F u t 1 9 f i r s t d i f f l a g 8 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 7 ) ;

876 ECM1. F u t 1 9 f i r s t d i f f l a g 9 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 8 ) ;

877 ECM1. F u t 1 9 f i r s t d i f f l a g 1 0 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 9 ) ;

878 ECM1. F u t 1 9 f i r s t d i f f l a g 1 1 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 1 0 ) ;

879 ECM1. F u t 1 9 f i r s t d i f f l a g 1 2 = l a g m a t r i x (ECM1. F u t 1 9 f i r s t d i f f l a g 1 , 1 1 ) ;

880 %Lag v a r i a b l e s s p o t :

881 ECM1. S p o t f i r s t d i f f l a g 1 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 1 ) ;

882 ECM1. S p o t f i r s t d i f f l a g 2 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 2 ) ;

883 ECM1. S p o t f i r s t d i f f l a g 3 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 3 ) ;

884 ECM1. S p o t f i r s t d i f f l a g 4 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 4 ) ;

885 ECM1. S p o t f i r s t d i f f l a g 5 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 5 ) ;

886 ECM1. S p o t f i r s t d i f f l a g 6 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 6 ) ;

887 ECM1. S p o t f i r s t d i f f l a g 7 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 7 ) ;

888 ECM1. S p o t f i r s t d i f f l a g 8 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 8 ) ;

889 ECM1. S p o t f i r s t d i f f l a g 9 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 9 ) ;

890 ECM1. S p o t f i r s t d i f f l a g 1 0 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 1 0 ) ;

891 ECM1. S p o t f i r s t d i f f l a g 1 1 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 1 1 ) ;

892 ECM1. S p o t f i r s t d i f f l a g 1 2 = l a g m a t r i x (ECM1. S p o t f i r s t d i f f , 1 2 ) ;

893

894 ECM 1 = f i t l m (ECM1, [’ S p o t f i r s t d i f f ˜ L a g g e d R e s i d u a l s + F u t 1 9 f i r s t d i f f l a g 1 + F u t 1 9 f i r s t d i f f l a g 2 ’ . . .

895 ’+ F u t 1 9 f i r s t d i f f l a g 3 + F u t 1 9 f i r s t d i f f l a g 4 + F u t 1 9 f i r s t d i f f l a g 5 + F u t 1 9 f i r s t d i f f l a g 6 ’ . . .

896 ’+ F u t 1 9 f i r s t d i f f l a g 7 + F u t 1 9 f i r s t d i f f l a g 8 + F u t 1 9 f i r s t d i f f l a g 9 + F u t 1 9 f i r s t d i f f l a g 1 0 ’ . . .

897 ’+ F u t 1 9 f i r s t d i f f l a g 1 1 + F u t 1 9 f i r s t d i f f l a g 1 2 + S p o t f i r s t d i f f l a g 1 + S p o t f i r s t d i f f l a g 2 ’ . . .

898 ’+ S p o t f i r s t d i f f l a g 3 + S p o t f i r s t d i f f l a g 4 + S p o t f i r s t d i f f l a g 5 + S p o t f i r s t d i f f l a g 6 ’ . . .

899 ’+ S p o t f i r s t d i f f l a g 7 + S p o t f i r s t d i f f l a g 8 + S p o t f i r s t d i f f l a g 9 + S p o t f i r s t d i f f l a g 1 0 ’ . . .

900 ’+ S p o t f i r s t d i f f l a g 1 1 + S p o t f i r s t d i f f l a g 1 2 ’] )

901

902 % Engle ’ s ARCH T e s t f o r ECM F19 :

903 ECM1. S q R e s i d u a l s = (ECM 1 . R e s i d u a l s . Raw) . ˆ 2 ;

904 ECM1. r e s 1 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 1 ) ;

905 ECM1. r e s 2 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 2 ) ;

906 ECM1. r e s 3 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 3 ) ;

907 ECM1. r e s 4 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 4 ) ;

908 ECM1. r e s 5 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 5 ) ;

909 ECM1. r e s 6 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 6 ) ;

910 ECM1. r e s 7 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 7 ) ;

911 ECM1. r e s 8 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 8 ) ;

912 ECM1. r e s 9 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 9 ) ;

913 ECM1. r e s 1 0 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 1 0 ) ;

914 ECM1. r e s 1 1 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 1 1 ) ;

915 ECM1. r e s 1 2 = l a g m a t r i x (ECM1. S q R e s i d u a l s , 1 2 ) ;

916

917 ECM1 = f i l l m i s s i n g (ECM1, ’ c o n s t a n t ’, 0 , ’ D a t a V a r i a b l e s ’, . . .

918 {’ r e s 1 ’,’ r e s 2 ’,’ r e s 3 ’,’ r e s 4 ’,’ r e s 5 ’,’ r e s 6 ’,’ r e s 7 ’, . . .

919 ’ r e s 8 ’,’ r e s 9 ’,’ r e s 1 0 ’,’ r e s 1 1 ’,’ r e s 1 2 ’}) ;

920

921 % Running t h e a u x i l i a r y r e g r e s s i o n

922 AuxReg1 = f i t l m (ECM1, [ ’ S q R e s i d u a l s ˜ r e s 1 + r e s 2 + r e s 3 + r e s 3 + r e s 4 + r e s 5 ’ . . .

923 ’+ r e s 6 + r e s 7 + r e s 8 + r e s 9 + r e s 1 0 + r e s 1 1 + r e s 1 2 ’] )

924

925 % T e s t i n g f o r a u t o c o r r e l a t i o n :

926 T = 1 6 8 7 ;

927 a l p h a = [ 0 . 1 , 0 . 0 5 , 0 . 0 1 ]

928 TestStatARCH = (T)∗AuxReg1 . Rsquared . O r d i n a r y

929 pVal = 1 − c d f ( ’ C h i s q u a r e ’, TestStatARCH , 1 2 )

930 c r i t i c a l A R C H = c h i 2 i n v (1−alpha , 1 2 ) ;

931 r e j e c t i o n = TestStatARCH > c r i t i c a l A R C H

932

933 % ECM−GARCH: Spot and Fut19 :

934 GARCH1 = g a r c h ( ’ GARCHlags ’, 1 , ’ ARCHlags ’, 1 )

935 [ estMdl , estParamCov , l o g L ] = e s t i m a t e (GARCH1, ECM1. S p o t f i r s t d i f f )

936 condVar = i n f e r ( estMdl , ECM1. S p o t f i r s t d i f f ) ;

937 ECM1. condVol = s q r t( condVar ) ;

938

939 ECM GARCH 1 = f i t l m (ECM1, [ ’ S p o t f i r s t d i f f ˜ L a g g e d R e s i d u a l s + F u t 1 9 f i r s t d i f f l a g 1 + F u t 1 9 f i r s t d i f f l a g 2 ’ . . .

940 ’+ F u t 1 9 f i r s t d i f f l a g 3 + F u t 1 9 f i r s t d i f f l a g 4 + F u t 1 9 f i r s t d i f f l a g 5 + F u t 1 9 f i r s t d i f f l a g 6 ’ . . .

941 ’+ F u t 1 9 f i r s t d i f f l a g 7 + F u t 1 9 f i r s t d i f f l a g 8 + F u t 1 9 f i r s t d i f f l a g 9 + F u t 1 9 f i r s t d i f f l a g 1 0 ’ . . .

942 ’+ F u t 1 9 f i r s t d i f f l a g 1 1 + F u t 1 9 f i r s t d i f f l a g 1 2 + S p o t f i r s t d i f f l a g 1 + S p o t f i r s t d i f f l a g 2 ’ . . .

943 ’+ S p o t f i r s t d i f f l a g 3 + S p o t f i r s t d i f f l a g 4 + S p o t f i r s t d i f f l a g 5 + S p o t f i r s t d i f f l a g 6 ’ . . .

944 ’+ S p o t f i r s t d i f f l a g 7 + S p o t f i r s t d i f f l a g 8 + S p o t f i r s t d i f f l a g 9 + S p o t f i r s t d i f f l a g 1 0 ’ . . .

945 ’+ S p o t f i r s t d i f f l a g 1 1 + S p o t f i r s t d i f f l a g 1 2 + condVol ’] )

946

947 f i g u r e;

948 p l o t(ECM1. Date , ECM1. S p o t f i r s t d i f f ) ;

949 h o l d on ;

950 p l o t(ECM1. Date , ECM1. condVol ) ;

951 h o l d o f f ;

952 l e g e n d(’ Log−d i f f e r e n c e d s p o t p r i c e ’, ’ I n f e r r e d v o l a t i l i t y ’) ;

953 box (’ o f f ’) ;

954

955 % F i n d i n g r e s i d u a l s between Spot and l a g g e d Fut18 :

956 r e g 2 = t a b l e ( ) ;

957 r e g 2 . Date = d a t a . Date ;

958 r e g 2 . Spot = d a t a . Spot ;

959 r e g 2 . LagFut18 = l a g m a t r i x ( d a t a . Fut18 , 1 ) ;

960 r e g 2 ( 1 , : ) = [ ] ;

961 r e g 2 ( 1 4 5 5 :end, : ) = [ ] ;

962 model2 = f i t l m ( r e g 2 , ’ Spot ˜ LagFut18 ’)

963 r e g 2 . r e s i d u a l s = model2 . R e s i d u a l s . Raw ;

964 p l o t( r e g 2 . Date , r e g 2 . r e s i d u a l s )

965

966 % D e f i n i n g ECM v a r i a b l e s − Spot and Fut18 :

967 ECM2 = t a b l e ( ) ;

968 ECM2. Date = r e g 2 . Date ;

969 ECM2. S p o t f i r s t d i f f = d a t a . S p o t f i r s t d i f f ( 2 : 1 4 5 5 ) ;

970 ECM2. L a g g e d R e s i d u a l s = l a g m a t r i x ( r e g 2 . r e s i d u a l s , 1 ) ;

971 %Lag v a r i a b l e s − Fut :

972 ECM2. F u t 1 8 f i r s t d i f f l a g 1 = r e g 2 . LagFut18 − l a g m a t r i x ( r e g 2 . LagFut18 , 1 ) ;