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Time Series Analysis

Time series analysis is a statistical technique that deals with time series data. In time series analysis, time series data means that data is in a series of a particular time period. In time series analysis, data is considered in three types:

Time series data: In time series analysis, time series data is a set of observations on the values that a variable takes at different times.                                  

Cross-sectional data: In time series analysis, Cross-section data is data of one or more variables, collected at the same point in time.

Pooled data: In time series analysis, pooled data is a combination of time series data and cross-sectional data.

Time series analysis terms and concepts:

Dependence: In time series analysis, dependence refers to the correlation of two observations with the same variable, at prior time points.

Stationarity: In time series analysis, stationarity shows the mean value of the series that remains constant over a time period.

Differencing: In time series analysis, differencing is used to make the series stationary, to De-trend, and to control the autocorrelations.

Specification: In time series analysis, specification may involve the testing of the linear or non-linear relationships of dependent variables by using models such as ARIMA, ARCH, GARCH, VAR, Co-integration, etc.

Exponential smoothing in time series analysis:

In time series analysis, exponential smoothing method predicts the one next period value based on the past and current value. In time series analysis, the exponential smoothing method is used to predict the short term predication. Alpha, Gamma, Phi, and Delta are the parameters that estimate the effect of the time series data. In time series analysis, alpha is used when seasonality is not present in data. In time series analysis, Gamma is used when a series has a trend in data. In time series analysis, delta is used when seasonality cycles are present in data. In time series analysis, a model is applied according to the pattern of the data. In time series analysis, the following models are available in SPSS: simple, Holt, winter, and custom. Exponential smoothing for time series analysis can be performed in SPSS by selecting “analysis → time series → exponential smoothing.”

Curve fitting in time series analysis:

In time series analysis, Curve fitting regression is used when data is in a non-linear relationship. The following equation shows the non-linear behavior:

Dependent variable, where case is the sequential case number.

Curve fitting for time series analysis can be performed by selecting “regression” from the analysis menu and then selecting “curve estimation” from the regression option.  Then select “wanted curve linear,” “power,” “quadratic,” “cubic,” “inverse,” “logistic,” “exponential,” or “other.”

ARIMA in time series analysis:

ARIMA in time series analysis stands for autoregressive integrated moving average method. This method is also known as the Box-Jenkins method.

Identification of ARIMA parameters:

Autoregressive component: In time series analysis, AR stands for autoregressive. In time series analysis, autocorrelation is denoted by p. When p =0, it means that there is no autocorrelation in the series. When p=1, it means that the series autocorrelation is till one lag.

Integrated: In ARIMA time series analysis, integrated is denoted by d. When d=0, it means the series is stationary and we do not need to take the difference of it. When d=1, it means that the series is not stationary and to make it stationary, we need to take the first difference. When d=2, it means that the series has been differenced twice. Usually, more than two time difference is not reliable.

Moving average component: In ARIMA time series analysis, MA stands for moving the average, which is denoted by q. In ARIMA, moving average q=1 means that it is an error term and there is autocorrelation with one lag.

In ARIMA model in time series analysis, in order to test weather or not the series and their error term is auto correlated, we usually use W-D test, ACF and PACF. To test the Stationarity of the series, unit test is preformed.

Decomposition: In time series analysis, decomposition refers to separating a time series into trend, cyclical, and irregular effects.

Assumptions in time series analysis:

Stationary: In time series analysis, the first assumption is that the series are stationary. This means that the series are normally distributed and the mean and variance are constant over a long time period.

Uncorrelated random error: In time series analysis, we assume that the error term is randomly distributed and the mean and variance are constant over a time period. The Durbin-Watson test is the standard test for correlated errors.

No outliers: In time series analysis, we assume that there is no outlier in the series. Outliers may affect conclusions strongly and can be misleading.

Random shocks: If shocks are present in the time series analysis, they are assumed to be randomly distributed with a mean of 0 and a constant variance.

Time Series Analysis Resources

Brockwell, P. J., & Davis, R. A. (1991). Time Series: Theory
            and Methods (2nd ed.). New York: Springer-Verlag.
Cromwell, J. B., Hannan, M. J., Labys, W. C., & Terraza, M. (1994). Multivariate tests for time series models. Thousand Oaks, CA: Sage Publications.
Cromwell, J. B., Labys, W. C., & Terraza, M. (1994). Univariate tests for time series models. Thousand Oaks, CA: Sage Publications.
Crosbie, J., & Sharpley, C. F. (1989). DMITSA: A simplified interrupted time-series analysis program. Behavior Research Methods, Instruments & Computers, 21(6), 639-642.
Gallistel, C. R. (1992). Classical conditioning as a nonstationary, multivariate time series analysis: A spreadsheet model. Behavior Research Methods, Instruments & Computers, 24(2), 340-351.
Hamaker, E. L., Dolan, C. V., & Molenaar, P. C. M. (2005). Statistical modeling of the individual: Rationale and application of multivariate stationary time series analysis. Multivariate Behavioral Research, 40(2), 207-233.
Hamilton, J. D. (1994). Time Series Analysis. Princeton, NJ: Princeton University Press.
McDowall, D., McCleary, R., Meidinger, E. E., & Hay, R. A., Jr. (1980). Interrupted time series analysis. Thousand Oaks, CA: Sage Publications.
Ostrom, C. W., Jr. (1990). Time series analysis: Regression techniques (2nd ed.). Thousand Oaks, CA: Sage Publications.
Sayrs, L. W. (1989). Pooled time series analysis. Newbury Park, CA: Sage Publications.
Strahan, R. (1973). A generalized directional coefficient for multiple time-series analysis. Multivariate Behavioral Research, 8(1), 109-116.
Velicer, W. F., & Fava, J. L. (2003). Time series analysis. In J. A. Schinka & W. F. Velicer (Eds.), Handbook of psychology: Research methods in psychology (pp. 581-606). Hoboken, NJ: John Wiley & Sons.
Yanovitzky, I., & VanLear, A. (2008). Time series analysis: Traditional and contemporary approaches. In A. F. Hayes, M. D. Slater, & L. B. Snyder (Eds.), The Sage sourcebook of advanced data analysis methods for communications research (pp. 89-124). Thousand Oaks, CA: Sage Publications.

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