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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.

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