How many observations will be lost in creating
1. a five period Moving Average model?
2. a 2nd-order Autoregressive model?
1. In a five period Moving Average model, the number of observations lost will be equal to the number of periods used for averaging minus one. Therefore, for a five period Moving Average model, four observations will be lost.
2. In a 2nd-order Autoregressive model, there will be no observations lost. The model uses past values of the same variable to predict the current value, so all observations can be used in the model without any being lost.
To calculate the number of observations that will be lost in creating a specific model, we need to consider the order of the model and the amount of data required for calculations.
1. For a five-period Moving Average model:
In a moving average model, each forecasted value is the average of the previous 'n' periods. To calculate the average for each period, we need a minimum of 'n' observations. In this case, we need five observations to calculate the first forecasted value. Therefore, we will lose the first four observations when creating a five-period Moving Average model.
2. For a 2nd-order Autoregressive model:
In an autoregressive model, each forecasted value is a weighted sum of the previous 'p' observations. To calculate the forecasted values, we need a minimum of 'p' observations. In this case, a second-order autoregressive model requires two observations to calculate the first forecasted value. Therefore, we will lose the first observation when creating a 2nd-order Autoregressive model.
To determine the number of observations that will be lost in creating different models, we need to understand the concepts and formulas for each model.
1. Five-period Moving Average model:
In a five-period Moving Average model, the average of the current observation and the previous four observations is taken as the estimated value for the given period. Since the Moving Average model requires historical data to calculate the average, the number of periods lost in creating this model is equivalent to the number of periods needed to calculate the moving average.
- For example, if you have a dataset with 100 observations, and you want to create a five-period Moving Average model, you will need to discard the first four observations because you cannot calculate the moving average for those periods.
Therefore, for a five-period Moving Average model, the number of observations lost would be 4.
2. Second-order Autoregressive model:
In a second-order Autoregressive (AR(2)) model, the value of the current observation is assumed to be a linear combination of the two previous observations, with some error term. The formula for an AR(2) model is:
X(t) = β0 + β1*X(t-1) + β2*X(t-2) + ε(t)
To estimate the parameters (β0, β1, and β2) of the AR(2) model, you need at least two observations for the lagged terms. Therefore, the number of observations lost in creating an AR(2) model is equivalent to the number of lagged terms used.
- For example, if you have a dataset with 100 observations and you want to create an AR(2) model, you would need to discard the first two observations because they do not have lagged terms available for calculation.
Therefore, for a second-order Autoregressive model (AR(2)), the number of observations lost would be 2.