The following problems will use a monthly data (not seasonally adjusted) on total clothing sales in the United States from January 1992 to December...

1.   The following problems will use a monthly data (not seasonally adjusted) on total clothing sales in the United States from January 1992 to December 2012. This data can be found from United States Census Bureau survey of "Monthly Retail Trade and Food Services" (category 4481).

1. Import the data into Stata from Excel. Generate and format your time variable for the monthly data. Let Stata know you are using time series data. Draw a time series graph of clothing sales (cloth) against time (your date variable). Comment on the various time series components of the graph.
2. Using Stata, generate the trend variable t (=_n). Now fit a deterministic trend model using the linear trend variable alone (when looking at the best trend model, do not include any other explanatory variables). Generate the information criteria, the fitted values graph, and the residuals graph.
3. Fit a quadratic trend model by adding t2 to the model in part b. Generate the information criteria, the fitted values graph, and the residuals graph. Explain which model (linear trend or quadratic trend) is the better trend model and why?

2.   We want to check if there is a break in the trend around the infamous Lehman Brothers crash in September 2008. Construct a dummy variable (D) that takes zeros before September 2008 and ones after that. Also, generate t×D, the interactive dummy variable, constructed as t ∗D. Choose the model that you picked in the previous question and add the trend dummy variable (D) and the interaction term (txD). All regressions are estimated over the sample period from January 1992 through December 2012.

1. Comment on the significance of difference in the intercept and the slope before and after September 2008. Test (jointly) if there is evidence of any structural break in the trend. Write down null and alternative hypothesis. Calculate the test statistic, carry out the test, and state your conclusions.
2. Draw a graph showing the shape of the trend suggested by the regression above. Draw a graph of the residuals and comment on the shape of the residuals. Is there any obvious pattern that we are missing in our model?
3. Create seasonal dummies for January through December to account for seasonality. Add to your previous model the seasonal dummies using December as the season of reference (i.e. dropping December to avoid the dummy variable trap). Generate the information criteria, the fitted values graph and the residuals graph. Comment on what the output is telling us about the seasonality present in the data. Does your answer to part a, change?
4. Write down the estimated regression equation from part c. Construct a 1-step ahead (January 2013) forecast for monthly clothing sales for the United States using this model