# Learning Center

A direct transformation of a time series can help you exploring your data and creating econometrics models in a blink of an eye. This is because you can use any variation of a time series in your model without having to insert the transformed time series in the spreadsheet. The list of transformations available in the Econometrics Toolbox is:

 Exp 2nd_Difference Power(n) Log Returns Fitted_AR(p) Sqrt AccumulatedReturns Fitted_MA(q) Normalization LogReturns Fitted_ARIMA(p,d,q) Abs AccumulatedLogReturns EWMA(lambda) Lag Square Fitted_Garch(p,q) Seasonal_Difference Series-Mean_Squared Error 1st_Difference

Using a transformation in your time series is just a matter of enclosing the transformation in the variable operators (Y[], X1[], X2[], … ) . Multiple operators are allowed, just type the transformations followed by a semicolon. Evaluations are made from the left to the right. So, for instance, Y[power(2); exp] will first apply the function f(x) = x^2 to every data x of the series denoted by Y and then apply the function g(f(x)) = exp(f(x)). As you can note, transformations that contain parenthesis need to have the letters enclosed replaced by appropriate parameters.

There is also one special transformation, the “error” transformation. This transformation returns the difference between the original series and the subsequent transformations until its evocation. Therefore, a transformation like Y[power(2); error] returns a transformed series Z = Y - Y^2, where Y is the original series in the spreadsheet.

All transformations are also available through the function “sTimeSeriesTransform” where you can simply type a transformation string — ex: “Y[log;power(2)]” — as one of the function's arguments.

To practice the above concepts a little bit, we are going to build a transformation to explore how the volatility of the following time series of some stock prices behaves, considering the series below:

 A B C D E F 1 Apple Inc. (Adjusted close price) 2 3 2012-12-31 71.03051 4 2013-01-02 73.28087 5 2013-01-03 72.3559 6 2013-01-04 70.34045 7 2013-01-07 69.92669 8 2013-01-08 70.11489 9 2013-01-09 69.01907 10 2013-01-10 69.87463 11 2013-01-11 69.44619 12 2013-01-14 66.97025 13 2013-01-15 64.85737 14 2013-01-16 67.54952 ... ... ... 746 2015-12-11 112.5692 747 2015-12-14 111.873 748 2015-12-15 109.8937 749 2015-12-16 110.7391 750 2015-12-17 108.3918 751 2015-12-18 105.4578 752 2015-12-21 106.7507 753 2015-12-22 106.6513 754 2015-12-23 108.0238 755 2015-12-24 107.447 756 2015-12-28 106.2435 757 2015-12-29 108.1531 758 2015-12-30 106.7408 759 2015-12-31 104.6919 760

We need the following chain of transformations: 1º- Transform price to log returns, 2º- Square the returns to get a measure of an instantaneous volatility, 3º smooth the volatility using the exponential weighted moving average model.

For the first transformation, we can use directly the “LogReturns” transformation or the pair 1st_Difference;Log. The second transformation can be done by the power(2) transformation or to be picky with volatility definition we can use the “Series-Mean_Squared” (the mean of logreturns is very close to zero for daily returns). Now, to smooth the results, we can apply an EWMA model with a decaying factor of 0.95, that is, use the transformation “EWMA(0.95)”. Putting it all together, we come to the following transformation string: Y[LogReturns;Power(2);EWMA(0.95)]. The screenshot of insertion box and the result is displayed below:

And double clicking the chart to expand it:

As a final remark, please note that when you have only one time series the explicitness of the operator Y[] is not necessary. Besides, the command window is not case sensitive. So, typing “Power” and “POWER” will lead to the same results.