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# Descriptive Stats

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data; The main aim is to summarize a data set, rather than use the data to learn about the population that the data are thought to represent.

Descriptive statistics provides simple summaries about the sample and about the observations that have been made. Such summaries may be either quantitative, i.e. summary statistics, or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of data as part of a more extensive statistical analysis, or they it may they are all that are necessary for a particular investigation.

The use of descriptive and summary statistics has an extensive history, and, indeed, the simple tabulation of populations and of economic data was the first way in which the topic of statistics appeared. More recently, a collection of summarisation techniques has been formulated under the heading of exploratory data analysis: an example of such a technique is the box plot.

## Use in time series analysis

- Distribution Analysis:
- Frequency distributions are depicted as a table or as a graph, one form of which is a histogram.
- Distribution properties:
- central tendency: mean, median, mode, etc.
- dispersion measure: range, mean absolute deviation, standard deviation, variance, inter-quartile, etc.
- Shape measure: Skew for symmetry, and Kurtosis for far-end tails.
- Unusual members of the population: Minimum, Maximum, Quartiles.

- Multivariate analysis: Multivariate analysis arises when more than one variable is measured for each member of a population. The main extra consideration here is that of association: the way in which the values of one subset of variables within a populations are related to other subsets: scatter plots, correlation and dependence, and conditional distribution.

## Remarks

- The lagged (i.e. Back shifted) time series can be considered as a separate variate, so multivariate statistics are used to summarize the association of the series with itself over time.

## Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740