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Midterm 1

# Midterm 1 - j = 1 2(f Derive the autocorrelation for all...

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Economics 467: Economic Forecasting State University of New York at Binghamton Department of Economics Spring 2010 Midterm I The exam consists of three questions on two pages. Each question is of equal value. 1. State (do not explain) whether or not the following series are stationary or non-stationary. In each case assume that ε t is a white noise sequence, t = 1 , 2 , . . . , T . (a) y t = 0 . 5 + ε t (b) y t = 1 . 5 + ε t (c) y t = 0 . 5 + ε t + 0 . 4 ε t 1 (d) y t = 0 . 5 + ε t + 1 . 4 ε t 1 (e) y t = 0 . 5 + ε t + 0 . 4 ε t 1 + 0 . 5 ε t 2 (f) y t = 0 . 5 + ε t + 0 . 4 ε t 1 + 0 . 5 ε t 2 + 0 . 1 ε t 3 (g) y t = 0 . 5 + 0 . 4 y t 1 + ε t (h) y t = 0 . 5 + 1 . 4 y t 1 + ε t (i) y t = 0 . 5 + 0 . 4 y t 1 + 0 . 5 y t 2 + ε t (j) y t = 0 . 5 + 0 . 4 y t 1 + 0 . 5 y t 2 + 0 . 1 y t 3 + ε t (k) y t = 0 . 5 + 0 . 4 y t 1 + 0 . 5 y t 2 + ε t + 0 . 4 ε t 1 + 0 . 5 ε t 2 2. Consider the following model: y t = μ + ε t + θ 2 ε t 2 (a) What is the common name for this model? (b) What type of data frequency would you expect to form this type of model. (c) Derive the expected value of the series. (d) Derive the variance of the series. (e) Derive the autocovariance of the series for all lags

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Unformatted text preview: j = 1 , 2 , . . . . (f) Derive the autocorrelation for all all lags j = 1 , 2 , . . . . Plot the autocorrelation function. (g) State the condition for which the model is invertible. (h) Assuming that the model is invertible, write it as an AR ( ∞ ). 1 Table 1: 3. Consider the EViews output for the time series regression of the series log( CPINSA t /CPINSA t − 4 ) where CPINSA contains quarterly values of the Consumer Price Index from 1961:Q1 to 2008:Q1. (a) Brie ﬂ y explain the relevance of using the series log( CPINSA t /CPINSA t − 4 ) as opposed to log ( CPINSA t ). (b) Why does EViews list the sample as starting from 1961:Q3 instead of 1961:Q1? (c) Is this series stationary? How do you know? (d) Is this series invertible? How do you know? 2...
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Midterm 1 - j = 1 2(f Derive the autocorrelation for all...

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