How do I convert a series to another base year? (index numbers, Laspeyres, Paasche)

In brief

How do I convert a series to another base year? The data assistant "Index numbers" (Edit data) creates a new column from it: change the base (new base = 100), change from the previous year, chain two series, price and quantity index by Laspeyres and Paasche.

How it works in Statable

On the data page choose "Edit data", then the assistant "Index numbers".
Choose the kind, for example "Change the base period (new base = 100)".
Choose the number column, the time column and the base period. The preview shows the first rows.
Check the name and choose "Create new column".

Change the base period

Each value is divided by the value of the base period and multiplied by 100. The base is a point in time or a whole year (then the mean of the year counts). If a value is missing in the base period or it is 0 or negative, Statable does not calculate and says why. Nothing is rounded.

Change from the previous year

The value is divided by the value of the previous year, multiplied by 100 and reduced by 100. The previous year is 12 places before for monthly values, 4 for quarters, 1 for yearly values, 52 for weeks. Statable recognises the spacing from the time column; it can be chosen under "More options". If there is no value from the previous year, it is a gap or it is 0, the cell stays empty; nothing is filled in. For daily or unevenly spaced points in time the value of the previous year is not unambiguous, so Statable does not calculate there.

Chain two series

An old and a new series that overlap at a common point in time become one series. Either the old series is converted to the new base or the new one to the old. If there are several common points in time, the last one applies unless you choose another. If there is none, Statable does not calculate and estimates nothing. Chaining assumes that both series measure the same thing. If the basket or the definition changes, a break remains in the series that chaining does not remove.

Laspeyres and Paasche

You need at least two goods, each with a column for the price and one for the quantity, and a base period.
Laspeyres holds the quantities of the base period fixed, Paasche takes the current quantities. Both give 100 for the base period.
The difference between the two shows how much the basket has shifted. It does not say which index is right.
The quantity index (Laspeyres) compares the quantities at the prices of the base period.
If a value is missing or a price is 0 or negative, that point in time is blocked; nothing is replaced.

Requirements and limits

Gaps are never filled in and never estimated. Where a required value is missing, the cell stays empty.
Without a time column Statable counts the rows in order, each row is one point in time. If one is missing in between, the result is wrong; a time column is better.
The result is a new column. An existing column is overwritten only if that is explicitly chosen.

Typical examples

Put a sales series on the year 2015 = 100.
Compare the price development of a basket by Laspeyres and by Paasche.

For specialists

Rebasing: I_t · 100 / mean of the base period. Previous year: x_t / x_(t-L) · 100 - 100 with L = 12, 4, 1, 52. Chaining to the new base: a_t · b_u / a_u; to the old: b_t · a_u / b_u. Laspeyres: Σ p_t q_0 / Σ p_0 q_0 · 100; Paasche: Σ p_t q_t / Σ p_0 q_t · 100; quantity index: Σ q_t p_0 / Σ q_0 p_0 · 100. Statable calculates it itself, checked against the R library micEconIndex and by hand.