time series

(redirected from Time series analysis)
Also found in: Dictionary, Thesaurus, Financial, Acronyms.

time series

[′tīm ‚sir·ēz]
A statistical process analogous to the taking of data at intervals of time.

time series

ideally, any set of data in which ‘a well-defined quantity is recorded at successive equally-spaced time points over a specific period’ (C. Marsh, 1988), e.g. the RETAIL PRICE INDEX. Where the data fail to fulfil all of these strict criteria, e.g. inadequately standardized variables, or gaps in the series, where the recording interval is not equally spaced, one may still speak of a time series if data over time are involved. However, the problems of interpretation of such a series will be much greater. An important source of time-series data is the CENSUS.

Time Series


an ordered set of statistical data that characterizes the change or development of a socioeconomic phenomenon over time. An example of a time series is presented in Table 1, which gives data on the production of electric power in the USSR during the period from 1928 to 1973.

The statistical data arranged sequentially in time are called the levels of the time series. The data should be comparable to one another, especially with respect to the territory covered,

Table 1. Production of electric power in the USSR from 1928 to 1973 (billions of kilowatt-hours)
1928 ..............5.0
1932 ..............13.5
1937 ..............36.2
1940 ..............48.3
1950 ..............91.2
1960 ..............292
1970 ..............741
1973 ..............915

range of objects embraced, methods of calculation, critical date, and structure. In an integral time series, the levels characterize the magnitude of the phenomena within certain intervals of time; in a moment time series, the phenomena are characterized at a certain date. The analysis of a time series involves several steps: the determination of the rate and intensity of development of the phenomenon under consideration, the finding of the basic trend of development, the measurement of the variability of the levels, the establishment of relationships with the development of other phenomena, and the performance of a comparative analysis of the development in different countries or regions.

The following statistics are defined for the analysis of dynamic series: absolute increases, rates of growth and increase, average levels of the series, average absolute increases, and average rates of growth and increase. The absolute increase is the difference between one level and the next, and the rate of growth is the ratio of the two levels. When expressed as a coefficient, the rate of increase is the difference between the rate of growth and unity; the rate of increase may also be expressed in percent. The average level of a series for interval series is defined as the arithmetic mean; for moment series it is defined by the formula

where is the average level, y1 is the initial level, yn is the final level, and η is the number of levels. The average absolute increase is defined as the quotient of the absolute increase for the entire period divided by the number of time units in the period. The average rate of growth can be computed in two ways: either as the geometric average of the rates of growth for the individual intervals of time or as the kth root of the growth rate for the entire period, where k is the number of time units in the period.

The trend is determined by smoothing. The variability of levels of a time series is measured by the mean square of the deviations of the actual levels from the trend. Relationships between the development of the given phonemenon and other phenomena are established by the method of time series correlation, which differs from the conventional correlation method by the possibility of autocorrelation, autoregression, variable correlation, and time lag. Different countries or regions are often analyzed comparatively through the use of a common basis: growth rates are determined for two or more countries for identical time intervals. It is best to calculate the statistics per capita when making a comparative analysis of development. The comprehensive analysis of time series permits identification of the patterns of development of the phenomena reflected in the series.


References in periodicals archive ?
Conflict of Interest: The first author being incharge of the Karachi's Road Traffic Injury Research and Prevention Center (RTIRPC) has signed the IRB statement declaring that ethical approval has been granted for the conduct of time series analysis on RTIRPC's data.
and Buda, A.S.: 2014, Time series analysis in the presence of coloured noise.
Despite these efforts, getting nonlinear time series analysis incorporated into actual practice has proven a slow and, for Sugihara, often frustrating process.
As the relative analysis cannot give satisfactory results even intuitively, we turn to the time series analysis. The whole regular business is separated by distance and truck type when the time series analysis is chosen.
The statistical techniques of time series analysis and spatial distribution allowed identifying the communities of Medellin with increased risk of death from TB and HIV in the years 2000 and 2007.
The current study applies time series analysis to assess the independent effect of treatment on demand on San Francisco's substance abuse treatment system.
Improvement of technological process control level can be achieved by the time series analysis in order to predict their future behaviour.
In the early years of GIS it may have made more sense to ignore the temporal component of geospatial data resources: there was little older content so time series analysis was out of the question anyway, barring massive and expensive vector digitizing of old maps.
Time Series Analysis and Cyclostratigraphy: Examining stratigraphic records of environmental cycles
In this study, chaos time series analysis, wavelet transform and waveform analysis are applied for recognizing the characteristics of the detected AE signals in the shearing of piano and stainless steel wires.
To that end, we focus on the elimination of the deterministic component in the time series analysis. The estimation of the deterministic component is carried out through GLS, as done by Elliot et al.
Parameter estimation and forecasting for univariate regression GARCH, asymmetric GARCH and EGARCH processes have been added to GI 3 (Time Series Analysis while Real and complex Jacobi preconditioners are now included in Fl 1 (Sparse Linear Algebra).