Consider the n 52 sales data on thermostat replacement comp

Consider the n = 52 sales data on thermostat replacement components given here. The annual data, are given in the file thermostat. Construct a time series plot of the data. Now set aside the last 4 observations for validation. Models are built based on the first 48 observations and are validated using last 4 observations. Regress sales on time, y_t = beta_0 + beta_1 t + epsilon_t, and use this regression to obtain the predictions and 95% prediction intervals for the next four observations. Investigate the adequacy of the linear trend model in part (a) by constructing appropriate residual diagnostics. Explain why this model does not appear to be an adequate representation. Consider the stochastic trend model, y_t = beta_0 + beta_1 y_t - 1 + epsilon_t Estimate the model coefficients; obtain the forecasts for the next four observations and obtain 95% prediction intervals. Consider a random walk for the errors and estimate the model in terms of its differences y_t + y_y - 1 = beta_1 + epsilon_t. Repeat the diagnostics. Obtain the forecasts for the next four periods, and obtain 95% prediction intervals. Which model performs best and why?

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