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All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

Web-Enabled Scientific Services & Applications
(C)opyright 2002-2022
written by Prof. dr. P. Wessa

Server date: June 25, 2022, 9:45 pm

This complicated online software application is the result of our continuous Research & Development efforts in the field of multidisciplinary Time Series Analysis in general and Financial Econometrics in particular. At the moment we cannot offer a complete reference manual due to the fact that the software is rapidly evolving, offering many new features and methods in a short period of time. A few simple examples however can be found here.

Below you can find an incomplete list of the features that are currently available in this module. Please, feel free to drop us a line if you have any suggestions or questions.

Example of Box-Jenkins Time Series Analysis
1select Browser or Excel in the first selection box (this specifies how the output is displayed)
2select Airline in the [data series] selection box
3select Spectrum/(P)ACF in the [command] selection box
4set L = 0 (this is the 'lambda' value of the Box-Cox transformation)
5set d = 1 (this is the non-seasonal differencing order)
6set D = 1 (this is the seasonal differencing order)
7set s = 12 (default value; this is the number of periods per year = seasonality)
8set K = 37 (this is the number of time lags to be computed)
9click the lower Execute button
10Now we can identify the ARMA model of the stationary time series. In this case we identify a non-seasonal MA(1) and a seasonal SMA(1) model. Hence, q=1 and Q=1.

General Commands
Edit dataEdit time series data (in textbox).
Meta dataEdit the meta data about the time series.

Specific Diagnostic Tools in Box-Jenkins ARIMA modeling
VRMCompute Variance Reduction Matrix.
SMPCompute Standard Deviation-Mean Plot.
ACFCompute Auto Correlation Function for K timelags.
ACF(d,D)Compute Auto Correlation Function for various degrees of non-seasonal differencing (d) and seasonal differencing (D).
PACFCompute Partial Auto Correlation Function for K timelags.
SpectrumCompute Normalized Cumulative Periodogram and Spectrum.
Spectrum/(P)ACFCompute the Auto Correlation Function, the Partial Auto Correlation Function, and the Normalized Cumulative Periodogram (Spectrum) for the time series under investigation.
EstimateCompute (estimate) all ARMA parameters (Full Information Maximum Likelihood Estimation).
ForecastCompute the Univariate Stochastic ARMA Forecast (Ceteris Paribus Forecast).

Simulation of Profit Densities
PDensityCompute the Profit Density of profits based upon a distribution-free simulation with 10*K = number of simulated profits, and M = 0 (default) for rejection of negative prices ('Metropolis' step). Note: do not set the number of K above 100 (= 1000 simulated profits) to save system resources.

General Descriptive Statistics
TimeplotCompute basic statistics and chart of time series values.
HistogramCompute histogram of time series values.
RootogramCompute suspended rootogram display of time series values.
Central TendencyCompute various types of averages.
ConcentrationCompute various types of concentration measures.
MomentsCompute centered and uncentered moments.
Skewness/KurtosisCompute and test various measures of Skewness and Kurtosis (small and large sample tests against normal distribution).
QuartilesCompute Quartiles based upon 8 different definitions.
PercentilesCompute Percentiles based upon 8 different definitions.
VariabilityCompute various measures of Variability for the time series.

Series types
original seriesApply analysis to the original (raw) time series after Box-Cox transform and differencing.
residual seriesApply analysis to the residuals of the ARMA model (void if no ARMA model has been estimated).
squared residualsApply analysis to the squared residuals of the ARMA model (void if no ARMA model has been estimated).
interpolationApply analysis to the interpolation forecast of the ARIMA model (void if no ARIMA model has been estimated).
stationary varianceApply analysis to W[t] = (lnY[t] - lnY[t-1]) (lnY[t] - lnY[t-1]) (this is used in the analysis of financial time series).
stationary rangeApply analysis to W[t] = |lnY[t] - lnY[t-1]| (this is used in the analysis of financial time series).
PD Buy and HoldApply analysis to the simulated Profit Density (PD) for the Buy&Hold strategy. Note: this assumes that the simulations have been previously computed.
PD Filter-ruleApply analysis to the simulated Profit Density (PD) for the Filter-rule strategy. Note: this assumes that the simulations have been previously computed.
PD BH - FilterApply analysis to the simulated difference in Profit Density (PD): Buy&Hold profits - Filter-rule profits. Note: this assumes that the simulations have been previously computed.

Parameter list
LLambda: parameter of the Box-Cox transformation function.
dDegree of non-seasonal differencing.
DDegree of seasonal differencing.
sSeasonality: number of observations per year.
KNumber of timelags to be used in computations (number of iterations in simulations = 10 K).
pDegree of non-seasonal AR(p) polynomial.
qDegree of non-seasonal MA(q) polynomial.
PDegree of seasonal SAR(P) polynomial.
QDegree of seasonal SMA(Q) polynomial.
Mset M = 1 to include a constant term (M = 0 otherwise)

Top | Output | References

To cite Wessa.net in publications use:
Wessa, P. (2022), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
Server : www.wessa.net

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