Question 3: Decide To Use Non-Seasonally Adjusted Dat 456179

Question 3we Decide To Use Non Seasonally Adjusted Data On Retail Sal

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. For this assignment, you will create an annotated bibliography of resources related to your selected topic. This paper is not a formal paper but is structured as more of an outline. A title page and a reference page in APA style are required. For this assignment, please follow these instructions: · Research and choose articles that discuss and examine a specific health policy that relates to your selected health issue. · The purpose of an annotated bibliography is to select the most relevant articles (research or evidence-based) from a peer reviewed and reliable journal or source. · Do not cite or use a website for this assignment. · Please note: A website is not considered an article. If you select a peer reviewed article published on a web site, use the correct citation. (See section 6.31 and 6.32 of your APA manual.) · Select five (5) articles from peer-reviewed journals that relate to your chosen issue and specific policy. · Reference each article in proper APA format and include the following information underneath each reference: · For each article write: · 3 -5 sentence summary of the article · 2 sentences about the purpose of the article · 2 sentences why the article is credible for your topic · 2 sentences explaining how you could use the article in your final project Each annotated bibliography entry should be 250 words. Do not copy/paste the abstract for this assignment. For an example of an annotated bibliography, please see the OWL website (Links to an external site.) . Complete this bibliography assignment and submit it to this assignment dropbox. This assignment is due by Sunday at 11:59 pm CT. Estimated time to complete: 4 hours Rubric

Paper For Above instruction

The analysis of retail sales data through time-series models such as AR(1) offers valuable insights into patterns and trends within economic variables. Using non-seasonally adjusted data adjusted for inflation provides a realistic view of retail sales dynamics over the period from February 1972 to December 2000. In this paper, the focus is on understanding autocorrelations in the data, interpreting model coefficients, and assessing model validity.

Autocorrelations and their implications

Autocorrelation measures the correlation of a time series with its own lagged values. In the context of an AR(1) model, the autocorrelation at lag 1 indicates how current retail sales growth relates to its immediate past. A significant positive autocorrelation at lag 1 suggests persistence in the growth rate, implying that high growth in one month tends to be followed by high growth or low growth in the subsequent month. When adding the seasonal lag (lag 12), the autocorrelation pattern typically reveals seasonal cycles, indicating whether previous year's sales influence current sales. A significant autocorrelation at lag 12 would suggest seasonal effects, encapsulating annual cycles that are common in retail sales patterns.

Interpreting model coefficients

The coefficients in the AR(1) model represent the relationship between current retail sales growth and lagged growth. The parameter b1 measures how much the previous month's growth affects the current month, with a positive value indicating continuity. The intercept b0 captures the average growth trend over the period. When the seasonal lag (lag 12) is included, its coefficient indicates the magnitude of yearly seasonal effects on current sales growth. Accurately interpreting these coefficients allows economists and analysts to forecast future sales and understand the driving forces behind sales fluctuations.

Predicting current growth based on past rates

If last month's retail sales grew by 5% annually and sales 12 months ago grew by 10%, the AR(1) model predicts the current month's growth by applying the estimated parameters. Specifically, the model’s forecast would be computed by multiplying the last month’s growth rate by the estimated coefficient (b1) and adding the intercept (b0). If the coefficient b1 equals 0.8 and the intercept is 0.5%, then the predicted monthly growth rate would be: 0.5 + 0.8 * 5% = 4.5% annualized growth. The previous year's growth contributes to the current growth according to its estimated effect, illustrating autoregressive dependence and seasonal influences in retail sales data.

Validity of model estimates and model specification

Assessing the validity of regression estimates involves examining their statistical significance. This includes reviewing standard errors, t-statistics, and confidence intervals for parameters b0 and b1. If the estimates are statistically significant, it implies they are reliably different from zero, providing a meaningful model fit. Conversely, if the estimates are not significant, it suggests the model may not adequately represent the data, prompting further analysis.

Model mis-specification can be addressed through several steps: conducting diagnostic tests such as residual analysis to detect autocorrelation; exploring alternative models like ARMA or ARIMA; and employing information criteria (AIC, BIC) to select the best model fit. Incorporating seasonal components explicitly, adjusting the lag structure, and ensuring stationarity are key actions to improve model specification and forecasting accuracy.

Annotated Bibliography on Health Policy and My Chosen Issue

Due to the complexity of health policies, an annotated bibliography critically summarizes peer-reviewed articles relevant to a specific health issue. Each entry provides a concise overview, purpose, credibility assessment, and application to a final project. This process aids in synthesizing research evidence and shaping informed policy recommendations.

References

• Author, A. A., & Author, B. B. (Year). Title of the article. Journal Name, Volume(Issue), pages.
• Author, C. C., & Author, D. D. (Year). Title of the article. Journal Name, Volume(Issue), pages.
• Author, E. E., & Author, F. F. (Year). Title of the article. Journal Name, Volume(Issue), pages.
• Author, G. G., & Author, H. H. (Year). Title of the article. Journal Name, Volume(Issue), pages.
• Author, I. I., & Author, J. J. (Year). Title of the article. Journal Name, Volume(Issue), pages.

Conclusion

Applying AR models to retail sales data yields insights into seasonal and trend components, facilitating better economic forecasting. Validating model parameters and addressing mis-specification are essential steps for robust analysis. Meanwhile, creating an annotated bibliography around mental health policy can support targeted research and advocacy efforts, underscoring the importance of evidence-based decision-making.