The file sales.dta contains 157 weekly observations on sales revenues (sales) and advertising expenditure (adv) in millions of dollars for a large US department store for 2005-2007. The weeks are from December 28, 2004, to December 25, 2007.
(a) Graph the series for sales. Does it appear to be stationary, trend stationary or stochastic?
(b) Formally test for the presence of a unit root. Explain what version of the test you used and why you used it.
(c) Examine the autocorrelation function and propose one or two possible models that may have generated the series.
(d) Estimate the model(s) proposed in part (c).
(e) Assess your model(s) using if possible formal tests and/or an information criterion. (f) Estimate the model you deem most appropriate and estimate it again on the first 100 observations.
(g) Generate forecasts for the next 57 observations, and plot forecasted and actual
observations. Assess the forecasting power of your model.
(h) Estimate a VAR model of sales and advertising. Be sure to justify your choice of lag length.
(i) Do sales Granger cause advertising or vice-versa of both? Carefully state the null hypothesis of any tests you employ and carefully state the conclusion.
(j) Generate a set impulse response functions and discuss their economic interpretation. (k) Generate a forecast of sales from the VAR and compare it to the univariate forecast of part g).
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