Slides34-2010

# Slides34-2010 - Time Series Models Lecture XXXIV Charles B...

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Time Series Models: Lecture XXXIV Charles B. Moss December 2, 2010 Charles B. Moss () Time Series Models December 2, 2010 1 / 22

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1 Nonspherical Errors - Autocorrelation in Structural Models 2 Time Series Models Fourier Models Autoregressive/Moving Average Models Charles B. Moss () Time Series Models December 2, 2010 2 / 22
Nonspherical Errors - Autocorrelation in Structural Models Time Series versus Structural Models I Theoretical models of supply and demand. F Most students have been introduced to the utility model for the derivation of consumer demand. Taking for example the Cobb-Douglas utility function max x 1 , x 2 x α 1 x β 2 s . t . p 1 x 1 + p 2 x 2 Y (1) Charles B. Moss () Time Series Models December 2, 2010 3 / 22

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Continued I Yields two demand equations x 1 ( p 1 , p 2 , Y ) = Y p 1 ± α α + β ² x 2 ( p 1 , p 2 , Y ) = Y p 2 ± β α + β ² . (2) Taking the natural logarithms of the demand equations in Equation 2 yields structural models of demand ln ( x 1 ) = ln ± α α + β ² - ln ( p 1 ) + ln ( Y ) ln ( x 2 ) = ln ± β α + β ² - ln ( p 2 ) + ln ( Y ) ³ ln ( x 1 ) = α 01 + α 11 ln ( p 1 ) + α 21 ln ( p 2 ) + α 31 ln ( Y ) ln ( x 2 ) = α 02 + α 12 ln ( p 1 ) + α 22 ln ( p 2 ) + α 32 ln ( Y ) ´ (3) Charles B. Moss () Time Series Models December 2, 2010 4 / 22
I The structural models can also be derived analytical expansions of theoretic relationships. Speciﬁcally, in production economics we derive the existence of the cost function for a ﬁrm (and the expenditure function for the consumer) ± min x x 0 w s . t . f ( x , y ) = 0 ² C ( w , y ) (4) often this relationship is estimated a second order Taylor series expansion of an unknown function C ( w , y ) = α 0 + α 0 x + 1 2 x 0 Ax + β 0 y + 1 2 y 0 By + x 0 Γ y . (5) The cost function and input demand functions derived using Shephard’s lemma are derived from economic theory. Charles B. Moss ()

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Slides34-2010 - Time Series Models Lecture XXXIV Charles B...

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