Why smooth time series data

Password Forgot your password? Smoothing of time series Smoothing of time series allows extracting a signal and forecasting future values. Simple exponential smoothing This model is sometimes referred to as Brown's Simple Exponential Smoothing , or the exponentially weighted moving average model. Holt-Winters seasonal additive model This method considers a trend that varies with time and a seasonal component with a period p. Holt-Winters seasonal multiplicative model This method ponders a trend that varies with time and a seasonal component with a period p.

Moving average This model is a simple way to take into account past and optionally future observations to predict values. Fourier smoothing The concept of the Fourier smoothing is to transform a time series into its Fourier coordinates, then remove part of the higher frequencies, and then transform the coordinates back to a signal.

View all tutorials. Download xlstat. Related features Time series descriptive statistics. Time series transformation. Mann-Kendall Trend Tests. Cointegration tests. Unit root and stationarity tests. Homogeneity tests for time series. So how good was the estimator for the amount spent for each supplier?

Let us compare the estimate 10 with the following estimates: 7, 9, and Performing the same calculations we arrive at: Estimator 7 9 10 Next we will examine the mean to see how well it predicts net income over time. The next table gives the income before taxes of a PC manufacturer between and The question arises: can we use the mean to forecast income if we suspect a trend?

A look at the graph below shows clearly that we should not do this. In summary, we state that The "simple" average or mean of all past observations is only a useful estimate for forecasting when there are no trends. That makes the plot have a more meaningful axis. The plot follows. For smoothing you should experiment with moving averages of different spans. Those spans of time could be relatively short. The objective is to knock off the rough edges to see what trend or pattern might be there.

Section 2. Of the alternative methods described in Section 2. The following plot is the smoothed trend line for the U. This puts a weight of. This is simple one-step ahead forecasting method that at first glance seems not to require a model for the data. Although the goal is smoothing and one step ahead forecasting, the equivalence to the ARIMA 0,1,1 model does bring up a good point.

We shouldn't blindly apply exponential smoothing because the underlying process might not be well modeled by an ARIMA 0,1,1. Continue in this fashion by successively substituting for the forecasted value on the right side of the equation.

This leads to:. Equation 2 shows that the forecasted value is a weighted average of all past values of the series, with exponentially changing weights as we move back in the series. We can examine the fit of the smooth by comparing the predicted values to the actual series. The data series is:. The exponential smoothing forecasting equation is.

The predicted value for the series at that time is.