# DMelt:Finance/Time Series

# Time series

DataMelt can read data (time series) in variety of formats, such as ASCII, Gauss and Matlab. One can read and write data in Microsoft Excel 97 formats (the extension "xls"). Data can be modified, showed as tables, plotted. Also, a statistical analysis can be performed. One can also save such data into ASCII, Gauss, Matlab,

The calculations with time series are based on the class HStatData.
Let us read data written in one of the popular formats, such as ASCII, Gauss, Matlab, Excel.

from jhpro.tseries import * js=HStatData("Data","http://datamelt.org/examples/data/jhpro/tseries/asciitest1.dat") js.toTable()

You will see a table with time series populated with the data. One can save this table back using "saveData" method:

from jhpro.tseries import * js=HStatData("Data","http://datamelt.org/examples/data/jhpro/tseries/asciitest1.dat") js.saveData("data.dat","txt")

We have specified "txt" (ASCII) format.One can also save data in Gauss, Matlab and Excel by specifying the appropriate string. Read HStatData class description.

For example, try the following methods:

js.saveData("aaa.mat","matlab") js.saveData("aaa.xls","Excel") js.saveData("aaa.gauss","GaussDat")

You can also convert HStatData to jhplot.PND and use the methods of PND. Finally, you can serialize HStatData into a compressed file, or XML using the Serialized class (see man:io:input_output).

You can read a number of example files into the time-series class. DMelt supports many file formats. Examples of supported files are located in the financial file format directory.

# Time series data formats

Data for time series are represented using the JMulti convention.

In case of ASCII data file, the file will look as:

/∗seasonally adjusted, West Germany: fixed investment, disposable income, consumption expenditures ∗/ 183 451 412 174 462 422 ... ...

The file should contain the data of each variable in a column, while missing values may be coded with NaN. The comment is optional.

There is another form of JMulTi which allows for easy data recognition without further user interaction. The following is an example of a ".dat" file with an optional description:

/∗seasonally adjusted, West Germany: fixed investment, disposable income, consumption expenditures ∗/ 3 1960.1 4 invest income cons 180 451 415 179 465 421 ... ...

where the first number defines the number of variables. The second number is the start date, and the last number the periodicity of the data set. The start date must be a valid date for the given periodicity. For example, 1960.1 stands for the first quarter of 1960 because 4 defines quarterly data. Yearly data has periodicity 1. The periodicity can be chosen to be any positive integer. It should be noticed that, for monthly data, January is coded with 1960.01, whereas 1960.1 or 1960.10 stands for October 1960.

Please read very good book Applied Time Series Econometrics.

# Plotting time series

Plotting of time series is not too difficult, assuming that you know how to work with jHPlot (or any other) canvases. You can convert 2 columns of data into the P1D class and use it to draw X vs Y:

from java.awt import Color,Font from jhplot import * from jhpro.tseries import * data= "http://datamelt.org/examples/data/jhpro/tseries/Canadian.dat" js=HStatData("Title",data) # look at 3rd and 0 columns p1=js.getP1D(3,0) # 3rd column for X, 9 column for Y print p1.toString() # check the data p1.setDrawLine(1) # show as connected lines p1.setTitle("Canadians") p1.setColor(Color.blue) # color blue # plot the data c1=HPlot("Canadians") c1.setNameX("RW") c1.setNameY("Prod") c1.visible() c1.setAutoRange() c1.draw(p1)

Here is a result of the output of the above code which reads time series:

Often, you would like to replace the labels of the X-axis so they will show the actual time. This trick was discussed in man:visual:plot_styles. Below you can find an example which makes the actual replacement:

from java.awt import Color,Font from jhplot import * from jhpro.tseries import * data= "http://datamelt.org/examples/data/jhpro/tseries/Canadian.dat" js=HStatData("Data",data) js.toTable() p1=js.getP1D(3,0) print p1.toString() p1.setDrawLine(1) p1.setTitle("Canadians") p1.setColor(Color.blue) c1=HPlot("Canadians") c1.setNameX("RW") c1.setNameY("Prod") c1.visible() c1.setAutoRange() c1.draw(p1) # now apply a replacement table # c1.setSubTicNumber(0,1) # reduce the number of subticks on X gs=c1.getGraphSettings() # settings for this graph gs.setAutomaticTicks(0,False) # do not want to recompute ticks for manual settings listX=gs.getLabelTicks(0) # obtain list of labels for ticks print "x=",listX # print all old labels. listX[0]="Jan" listX[1]="Feb" listX[2]="Mar" listX[3]="Apr" listX[4]="May" listX[5]="Jun" listX[6]="Jul" listX[7]="Aug" listX[8]="Sep" listX[9]="Oct" listX[10]="Nov" gs.setLabelTicks(0,listX) c1.update()

# Descriptive statistics

One can do a full-scale analysis of time series using many powerful methods described below. Here is a 6-line Python macro which extracts one column from a data series and performs a detailed statistical analysis:

To do this, it makes sense to convert columns in jhplot.P0D representation and use its methods.

from jhplot import * from jhpro.tseries import * js=HStatData("Title","http://datamelt.org/examples/data/jhpro/tseries/Canadian.dat") p=js.getP0D(1) # look the 2nd column print p.toString() # check this column print p.getStatString() # print statistics

The output of this short script is given below. As you can see, it prints mean,. RMS, variance, Standard deviation, min and max values, Skewness, kurtosis and high order moments:

Size: 88 Sum: 79317.60942234722 SumOfSquares: 7.490318884164342E7 Min: 0.0 Max: 961.765709811429 Mean: 901.3364707084911 RMS: 922.5901584523979 Variance: 39210.743676671525 Standard deviation: 198.0170287542754 Standard error: 21.10868619051051 Geometric mean: 0.0 Product: 0.0 Harmonic mean: 0.0 Sum of inversions: Infinity Skew: -4.275748299773066 Kurtosis: 16.51526905197178 Sum of powers(3): 7.074101996131584E10 Sum of powers(4): 6.681632756449685E13 Sum of powers(5): 6.3115221764760856E16 Sum of powers(6): 5.962464385763685E19 Moment(0,0): 1.0 Moment(1,0): 901.3364707084911 Moment(2,0): 851172.6004732207 Moment(3,0): 8.038752268331345E8 Moment(4,0): 7.592764495965552E11 Moment(5,0): 7.172184291450098E14 Moment(6,0): 6.7755277110950963E17 Moment(0,mean()): 1.0 Moment(1,mean()): -5.6843418860808015E-14 Moment(2,mean()): 38765.16704398216 Moment(3,mean()): -3.3198598540862594E7 Moment(4,mean()): 3.0004383082685673E10 Moment(5,mean()): -2.704012982455758E13 Moment(6,mean()): 2.4372448867975816E16 25%, 50%, 75% Quantiles: 933.6877992686658, 945.85509828759, 949.9494485185958 quantileInverse(median): 0.5056818181818115

# Time series analysis

Time series can be analyzed in many different approaches by extraction columns and rows of the data. In particular, you can construct autocorrelation and cross-correlation vectors. and plot them. One can also perform Gaussian filtering and detect peaks using a peak finder algorithm.

You can extract the columns of data using "getColumn(int column)" method applied to the HStatData data holder. Then use different statistical procedures to discover the data:

Please look at the class HStatAnalysis to construct autocorrelation and cross-correlation by using HStatData directly.

See the package summary jhpro.tseries.package-summary

# Time series transformations

Time series can be transformed using an analytic functions. Essentially, you can construct a function of any complexity using functions using the same syntax as for 1D functions jhplot.F1D. Find below a stript which transforms the first column of the time series container using the function $1+\sqrt(x)$

from java.awt import Color,Font from jhplot import * from jhpro.tseries import * data= "http://datamelt.org/examples/data/jhpro/tseries/Canadian.dat" js=HStatData("Data",data) js.toTable() # show this time series a=HStatAnalysis(js); a.transformColumn(0,"1+sqrt(x)") # make a transformation of the first column p1=js.getP1D(3,0) print p1.toString() # just checking p1.setDrawLine(1) p1.setTitle("1+sqrt(x)") p1.setColor(Color.blue) c1=HPlot("Canadians 1+sqrt(x)") c1.setNameX("RW") c1.setNameY("1+sqrt(Prod)") c1.visible() c1.setAutoRange() c1.draw(p1)

# Histograms

To show an column as a histogram is a convenient way to sudy the properties of time series. Below we show how to convert a column to jhplot.H1D histogram and show it on the canvas:

from java.awt import Color,Font from jhplot import * from jhpro.tseries import * data= "http://datamelt.org/examples/data/jhpro/tseries/Canadian.dat" js=HStatData("Data",data) js.toTable() a=HStatAnalysis(js); h=a.getH1D(2,20,5,15) h.setTitle("Histogram of U column") h.setFill(1) h.setFillColor(Color.red) c1=HPlot("Column 3") c1.setNameX("RW") c1.setNameY("U") c1.visible() c1.setAutoRange() c1.draw(h)

The output of this code is shown below.