# Introduction

### Time Series Interpolation and Frequency Conversion

The EXPAND procedure provides time interval conversion and missing value interpolation for time series. The EXPAND procedure includes the following features:

• conversion of time series frequency; for example, constructing quarterly estimates from annual series or aggregating quarterly values to annual values

• conversion of irregular observations to periodic observations

• interpolation of missing values in time series

• conversion of observation types; for example, estimate stocks from flows and vice versa. All possible conversions are supported between any of the following:

• beginning of period

• end of period

• period midpoint

• period total

• period average

• conversion of time series phase shift; for example, conversion between fiscal years and calendar years

• identifying observations including the following:

• identification of the time interval of the input values

• validation of the input data set observations

• computation of the ID values for the observations in the output data set

• choice of four interpolation methods:

• cubic splines

• linear splines

• step functions

• simple aggregation

• ability to perform extrapolation by a linear projection of the trend of the cubic spline curve fit to the input data

• ability to transform series before and after interpolation (or without interpolation) by using any of the following:

• constant shift or scale

• sign change or absolute value

• logarithm, exponential, square root, square, logistic, inverse logistic

• lags, leads, differences

• classical decomposition

• bounds, trims, reverse series

• centered moving, cumulative, or backward moving average

• centered moving, cumulative, or backward moving range

• centered moving, cumulative, or backward moving geometric mean

• centered moving, cumulative, or backward moving maximum

• centered moving, cumulative, or backward moving median

• centered moving, cumulative, or backward moving minimum

• centered moving, cumulative, or backward moving product

• centered moving, cumulative, or backward moving corrected sum of squares

• centered moving, cumulative, or backward moving uncorrected sum of squares

• centered moving, cumulative, or backward moving rank

• centered moving, cumulative, or backward moving standard deviation

• centered moving, cumulative, or backward moving sum

• centered moving, cumulative, or backward moving median

• centered moving, cumulative, or backward moving t-value

• centered moving, cumulative, or backward moving variance

• support for a wide range of time series frequencies:

• YEAR

• SEMIYEAR

• QUARTER

• MONTH

• SEMIMONTH

• TENDAY

• WEEK

• WEEKDAY

• DAY

• HOUR

• MINUTE

• SECOND

• support for repeating of shifting the basic interval types to define a great variety of different frequencies, such as fiscal years, biennial periods, work shifts, and so forth

Refer to Chapter 3: Working with Time Series Data, and Chapter 4: Date Intervals, Formats, and Functions, for more information about time series data transformations.