Which of the following statements about autoregressive model is true?
Group of answer choices
It does regression automatically
It takes advantage of autocorrelation between values in different periods
The degrees of freedom for a p-th order autoregressive model is n-p-1
None of the others
The statement "It takes advantage of autocorrelation between values in different periods" is true for an autoregressive model. This model uses the relationship between an observation and a certain number of lagged observations to predict future values. By taking into account the autocorrelation between values in different periods, it can capture the underlying patterns and dynamics of the time series data.
The statement "It takes advantage of autocorrelation between values in different periods" is true for an autoregressive model. Autoregressive models use the dependency of an observation on previous observations to predict future values. By considering the autocorrelation between values in different periods, autoregressive models capture the temporal relationship between the observations.
To determine which statement about autoregressive models is true, let's evaluate each statement one by one:
1. "It does regression automatically": This statement is not accurate. Autoregressive models are a type of regression model, but they do not perform regression automatically. Instead, autoregressive models capture the relationship between a variable and its previous values.
2. "It takes advantage of autocorrelation between values in different periods": This statement is true. Autoregressive models are designed to model the autocorrelation, which is the relationship between observations at different time points. This can be beneficial when predicting future values based on past values.
3. "The degrees of freedom for a p-th order autoregressive model is n-p-1": This statement is also true. The degrees of freedom for an autoregressive model of order p are calculated as n - p - 1, where n is the number of observations in the dataset. The degrees of freedom represent the number of independent pieces of information available for estimating the parameters of the model.
Based on the explanations provided, the second statement, "It takes advantage of autocorrelation between values in different periods," is the correct answer.