the one now being forecast is not known, so its expected value—the predicted value arising from the previous forecasting step—is used instead. Then for future periods the same procedure is used, each time using one more forecast value on the right side of the predictive equation until, after p predictions, all p right-side values are predicted values from preceding steps. There are four sources of uncertainty regarding predictions obtained in this manner: (1) uncertainty as to whether the autoregressive model is the correct model; (2) uncertainty about the accuracy of the forecasted values that are used as lagged values in the right side of the autoregressive equation; (3) uncertainty about the true values of the autoregressive coefficients; and (4) uncertainty about the value of the error term for the period being predicted. Each of the last three can be quantified and combined to give a confidence interval for the n-step-ahead predictions; the confidence interval will become wider as n increases because of the use of an increasing number of estimated values for the right-side variables. Evaluating the quality of forecasts The predictive performance of the autoregressive model can be assessed as soon as estimation has been done if cross-validation is used. In this approach, some of the initially available data was used for parameter estimation purposes, and some (from available observations later in the data set) was held back for out-of-sample testing. Alternatively, after some time has passed after the parameter estimation was conducted, more data will have become available and predictive performance can be evaluated then using the new data. In either case, there are two aspects of predictive performance that can be evaluated: one-step-ahead and n-step-ahead performance. For one-step-ahead performance, the estimated parameters are used in the autoregressive equation along with observed values of X for all periods prior to the one being predicted, and the output of the equation is the one-step-ahead forecast; this procedure is used to obtain forecasts for each of the out-of-sample observations. To evaluate the quality of n-step-ahead forecasts, the forecasting procedure in the previous section is employed to obtain the predictions. Given a set of predicted values and a corresponding set of actual values for X for various time periods, a common evaluation technique is to use the mean squared prediction error; other measures are also available (see forecasting#forecasting accuracy). The question of how to interpret the measured forecasting accuracy arises—for example,