Time series analysis may be a statistical technique that deals with statistic data, or analysis. Statistic data means data is during a series of particular time periods or intervals. The info is taken into account in three types:
Time series data: a group of observations on the values that a variable takes at different times.
Cross-sectional data: Data of 1 or more variables, collected at an equivalent point in time.
Pooled data: a mixture of your time series data and cross-sectional data.
Terms and concepts:
Dependence: Dependence refers to the association of two observations with an equivalent variable, at prior time points.
Stationarity: Shows the mean of the series that is still constant over a time period; if past effects accumulate and therefore the values increase toward infinity, then stationarity isn’t met.
Differencing: wont to make the series stationary, to De-trend, and to regulate the auto-correlations; however, a while series analyses don’t require differencing and over-differenced series can produce inaccurate estimates.
Specification: May involve the testing of the linear or non-linear relationships of dependent variables by using models like ARIMA, ARCH, GARCH, VAR, Co-integration, etc.
Exponential smoothing in statistic analysis: This method predicts the one next period value supported the past and current value. It involves averaging of knowledge such the nonsystematic components of every individual case or observation wipe out one another. The exponential smoothing method is employed to predict the short term predication. Alpha, Gamma, Phi, and Delta are the parameters that estimate the effect of the statistic data. Alpha is employed when seasonality isn’t present in data. Gamma is employed when a series features a trend in data. Delta is employed when seasonality cycles are present in data. A model is applied consistent with the pattern of the info. Curve fitting in statistic analysis: Curve fitting regression is employed when data is during a non-linear relationship. The subsequent equation shows the non-linear behavior:
Dependent variable, where case is that the sequential case number.
Curve fitting are often performed by selecting “regression” from the analysis menu then selecting “curve estimation” from the regression option. Then select “wanted curve linear,” “power,” “quadratic,” “cubic,” “inverse,” “logistic,” “exponential,” or “other.”
ARIMA:
ARIMA stands for autoregressive integrated moving average. This method is additionally referred to as the Box-Jenkins method.
Identification of ARIMA parameters:
Autoregressive component: AR stands for autoregressive. Autoregressive parameter is denoted by p. When p =0, it means there’s no auto-correlation within the series. When p=1, it means the series auto-correlation is until one lag.
Integrated: In ARIMA statistic analysis, integrated is denoted by d. Integration is that the inverse of differencing. When d=0, it means the series is stationary and that we don’t got to take the difference of it. When d=1, it means the series isn’t stationary and to form it stationary, we’d like to require the primary difference. When d=2, it means the series has been differenced twice. Usually, quite two time difference isn’t reliable.
Moving average component: MA stands for moving the typical, which is denoted by q. In ARIMA, moving average q=1 means it’s a mistake term and there’s auto-correlation with one lag.
In order to check whether or not the series and their error term is auto correlated, we usually use W-D test, ACF, and PACF.
Decomposition: Refers to separating a statistic into trend, seasonal effects, and remaining variabilityAssumptions:
Stationarity: the primary assumption is that the series are stationary. Essentially, this suggests that the series are normally distributed and therefore the mean and variance are constant over an extended period of time.
Uncorrelated random error: We assume that the error term is randomly distributed and therefore the mean and variance are constant over a period of time. The Durbin-Watson test is that the standard test for correlated errors.
No outliers: We assume that there’s no outlier within the series. Outliers may affect conclusions strongly and may be misleading.
Random shocks (a random error component): If shocks are present, they’re assumed to be randomly distributed with a mean of 0 and a continuing variance.
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