Trend Models for the Prediction of Economic Cycles
Many different approaches have been proposed to deal with the signal extraction problem in general. In line with this problem, trend estimation has also received a great deal of attention in the time series literature, especially when the interest is focused on forecasting turning points. In spite of all the differences among methods, one common feature remains in most of them. This is that trends tend to extrapolate themselves into the future as a line with a slope that depends on the recent past information. Although this is an optimal (e.g. in a Mean Square Error sense) and a sensible way to do it, it can be systematically erroneous when turning points are at hand. Nor those trend changes could be detected. In those situations, the main source of forecast errors is due to the trend. In this paper two linear trend models with a non-linear like forecast function are explored, namely the Smoothed Random Walk and the Double Integrated Autoregressive model. A combination of two frequency domain methods are explored as the procedure for the identification and estimation of these models. The trend models are compared with standard ones and its forecast performance tested on several real time series examples.
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