Consider the daily simple returns of IBM stock from 1970 to 2008 in the file d-i

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Consider the daily simple returns of IBM stock from 1970 to 2008 in the file d-ibm3dx7008.txt. Compute the first 100 lags of ACF of the absolute series of daily simple returns of IBM stock. Is there evidence of long-range dependence? Why?

Consider the demand of electricity of a manufacturing sector in the United States. The data are logged, denote the demand of a fixed day of each month, and are in power6.txt. Build a time series model for the series and use the fitted model to produce 1- to 24-step-ahead forecasts.

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To compute the first 100 lags of the ACF of the absolute series of daily simple returns of IBM stock, you would need to first calculate the absolute value of each daily simple return. Then, you would use the autocorrelation function (ACF) to calculate the correlation between the absolute daily simple returns and lags of those returns. The resulting ACF values would show how much the absolute daily simple returns at a given lag are correlated with the absolute daily simple returns at different lags.

To determine if there is evidence of long-range dependence, you would need to examine the ACF values at the longer lags. If the ACF values at the longer lags are still significant, it would indicate that there is long-range dependence in the series. However, without the data, it is impossible for me to tell if there is long-range dependence or not.

Regarding the second question, to build a time series model for the demand of electricity of a manufacturing sector in the United States, you would need to first examine the data to determine the appropriate type of model. The data provided is logged, indicating that it may be suitable for modeling using a log-transformed time series model, such as a log-transformed ARIMA model.

Once the model is built, it can be used to produce 1- to 24-step-ahead forecasts. This can be done by inputting the most recent data points into the model and forecasting the next 1- to 24 steps. However, the accuracy of the forecast depends on the quality of the model, which is why it is important to have a good understanding of the data and choose the appropriate model.