Autocorrelations adding seasonal lag of sales growth to interpret the coefficients in the model 3)Retail sales growing at a certain rate per month and involving the model to estimate a growt

Question 3:

We decide to use non-seasonally adjusted data on retail sales, adjusted for inflation. To begin with, we

estimate an AR(1) model with observations on the annualized monthly growth in real retail sales from

February 1972 to December 2000. We estimate the following equation:

Table 5 shows the results from this model:

A) What do the autocorrelations show and why?

B) Suppose we add the seasonal lag of sales growth (the 12th lag) to the AR(1) model to estimate the

equation:

Table 6 presents the results.

What do the autocorrelations show and why?

C) How can we interpret the coefficients in the model?

D) If retail sales grew at an annual rate of 5 percent last month and at an annual rate of 10 percent 12

months ago, the model predicts that retail sales will grow in the current month at an annual rate of?

Question 4:

A. Using the regression output in the above table, determine whether the estimates for b0 and b1 are

valid.

B. If this model is mis-specified, describe the steps we should take to determine the appropriate

autoregressive time-series model for these data.

USEFUL NOTES FOR:

As you can see from the attached document, question 3 concerns non-seasonally adjusted data adjusted for inflation, and an equation used to estimate 1) Autocorrelations 2) adding seasonal lag of sales growth to interpret the coefficients in the model

Introduction

In this question, you will be asked to analyze non-seasonally adjusted data and calculate the coefficient of correlation.

Autocorrelations

Autocorrelations are the correlation between a variable and its own lagged value. The autocorrelation function is the correlation between a variable and its own lagged values, calculated at different lag lengths. The first y-axis shows how much each value affects the next one; for example, if you look at what happens when you add $100 to your income over time, the first year of your income has no effect on the second year’s income (the slope on that line is 0).

The second y-axis shows how much each value affects future values; for example, if at any given point in time I earn $400/year but then later my salary goes up by 10% every year since then—and so does inflation—then over five years my salary will be around $450!

adding seasonal lag of sales growth to interpret the coefficients in the model

Adding seasonal lag of sales growth to interpret the coefficients in the model

The purpose of adding seasonal lag of sales growth to interpret the coefficients in the model is to account for price changes during a particular period, which may be different from what you would expect based on your knowledge about how consumers react over time. For example: If you know that consumers typically spend more money on utility bills during winter months than they do at other times of year, then adding this variable could help determine whether there are any seasonal patterns that should be accounted for when interpreting these data.

As you can see from the attached document, question 3 concerns non-seasonally adjusted data adjusted for inflation, and an equation used to estimate

As you can see from the attached document, question 3 concerns non-seasonally adjusted data adjusted for inflation, and an equation used to estimate

Autocorrelations. The model includes a seasonal lag term that accounts for the annual variation in sales growth. We will use this model to estimate the coefficients in Table 4 of our analysis.

Conclusion

Thank you for taking the time to do this research, and I am sure you will find it useful. Feel free to contact me if there are any questions or concerns.