Function reference

convert(s, to, [method], [partial]) · operation key convert

Converts the series to another frequency. To a lower frequency (e.g. monthly → quarterly) the values of each period are aggregated. 'Automatic' (default) follows the kind of indicator: flows such as GDP, exports or budget revenue are summed, end-of-period stocks such as debt take the last value, and rates, indices, prices and indicators of unknown kind are averaged; the method applied is shown in the series history. The method can also be chosen: average, sum (flows such as GDP or exports), last value (end-of-period stocks such as debt), first value, maximum or minimum. To a higher frequency (e.g. annual → quarterly) the values are interpolated linearly or with a cubic spline (each value placed at the end of its period), repeated (constant) or distributed equally so that sums are preserved (distribute). Choosing sum, average or last when converting to a higher frequency distributes, repeats or interpolates respectively. Incomplete periods at the start or end are dropped unless 'Include incomplete periods' is ticked. Weeks belong to the month, quarter or year that contains their Thursday (ISO 8601).

convert(s1, "Q", "average")

convert(s1, "A", "sum")

convert(s1, "M", "linear")

wavg(s1, s2, …, weights, [normalize]) · operation key weighted_average

Weighted average of several series of the same frequency: Σ wᵢ·sᵢ / Σ wᵢ (weights in the order of the series). With 'Normalise weights' switched off the weighted sum Σ wᵢ·sᵢ is returned. A period is missing if any of the series is missing in it.

wavg(s1, s2, weights=[0.6, 0.4])

wavg(s1, s2, s3, weights=[1, 2, 1], normalize=false)

lag(s, [n]) · operation key lag

Moves the series n periods later in time: the value at period t equals the original value at t − n (the whole series is kept and ends n periods later). A negative n works as a lead.

lag(s1, 1)

lag(s1, 4)

lead(s, [n]) · operation key lead

Moves the series n periods earlier in time: the value at period t equals the original value at t + n. A negative n works as a lag.

lead(s1, 1)

lead(s1, 12)

shiftyears(s, [years]) · operation key shift_years

Moves the whole series n years forward on the time axis (backwards if n is negative), so that different years of the same series can be overlaid in one chart or table, e.g. this year's monthly path against last year's (shift_years(s, 1)).

shiftyears(s1, 1)

shiftyears(s1, -1)

window(s, [start], [end]) · operation key window

Keeps only the observations from the start to the end period (inclusive); either bound may be left empty. Combined with Shift by years and statistics it compares different periods of the same series. Periods may be written as 2008, 2008-S1, 2008-Q1, 2008-03, 2008-W10 or 2008-03-15; a year selects all its quarters, months or days.

window(s1, "2008-Q1", "2012-Q4")

window(s1, "2015")

cumulative(s, [func], [reset]) · operation key cumulative

Accumulates the values over time: cumulative sum, product, running maximum, minimum or average. With restart 'every year' the accumulation starts again each calendar year (year-to-date). A missing value interrupts a sum, product or average (until the next year when restarting yearly); fill gaps first if needed.

cumulative(s1, "sum")

cumulative(s1, "sum", "year")

max(s1, s2, …) · operation key max_series

Largest value of several series of the same frequency in each period (missing if any series is missing in that period).

max(s1, s2)

mean(s1, s2, …, [skipna]) · operation key mean_series

Simple (unweighted) average of several series of the same frequency, period by period. By default a period is missing if any series is missing; with 'Ignore missing values' the available values are averaged.

mean(s1, s2)

mean(s1, s2, s3, skipna=true)

min(s1, s2, …) · operation key min_series

Smallest value of several series of the same frequency in each period (missing if any series is missing in that period).

min(s1, s2)

rolling(s, [window], [func], [min_periods]) · operation key rolling

At each period aggregates the last n observations (trailing window): moving average, moving sum, minimum, maximum, median or standard deviation, e.g. the 12-month moving sum of monthly exports. By default the full window must have values.

rolling(s1, 12, "sum")

rolling(s1, 4)

rolling(s1, 12, "std")

sum(s1, s2, …, [skipna]) · operation key sum_series

Adds several series of the same frequency period by period (e.g. the sum of regional or sectoral components). By default a period is missing if any series is missing; with 'Ignore missing values' the available values are added.

sum(s1, s2, s3)

sum(s1, s2, skipna=true)

ytd(s, [func]) · operation key ytd

Cumulative sum or average from the beginning of each calendar year, e.g. budget revenue since January. A year whose earlier periods are missing has no year-to-date values.

ytd(s1, "sum")

ytd(s1, "mean")

change(s, [kind], [horizon], [n], [annualize]) · operation key change

Change over a chosen horizon: absolute (x_t − x_{t−k}), percentage (100·(x_t / x_{t−k} − 1)), logarithmic (ln x_t − ln x_{t−k}), logarithmic × 100 or ratio (x_t / x_{t−k}). The horizon is the previous period, a month, a quarter, a year or a custom number of periods; k = n × horizon. 'Annualise' expresses the change as an annual rate (compounded for percentage changes and ratios). For daily data the previous observation is used, and month/quarter/year horizons use the last observation on or before the same date.

change(s1, "pct", "year")

change(s1, "abs", "period")

change(s1, "log_pct", "quarter", 1, true)

changeref(s, ref, [kind]) · operation key change_ref

Change of every value relative to the value at a chosen reference period, e.g. 2019-Q4 as the pre-pandemic level: percentage, absolute, ratio or logarithmic. If the reference is a longer period than the data (e.g. a year for quarterly data), its average is used.

changeref(s1, "2019-Q4", "pct")

changeref(s1, "2019", "abs")

diff(s, [n]) · operation key diff

Absolute change from n periods earlier: x_t − x_{t−n} (for daily data: n observations earlier).

diff(s1)

diff(s1, 4)

logdiff(s, [n], [scale]) · operation key log_diff

Logarithmic change scale·(ln x_t − ln x_{t−n}); with the default scale 100 it approximates the percentage change. Zero or negative values give empty results.

logdiff(s1)

logdiff(s1, 12)

logdiff(s1, 1, 1)

mom(s) · operation key pct_mom

Percentage change from the previous month: 100·(x_t / x_{t−1} − 1). Monthly data only.

mom(s1)

qoq(s, [annualize]) · operation key pct_qoq

Percentage change from the previous quarter; for monthly data the change from three months earlier. Optionally annualised: 100·((x_t / x_{t−1})⁴ − 1).

qoq(s1)

qoq(s1, true)

yoy(s) · operation key pct_yoy

Percentage change from the same period of the previous year: 100·(x_t / x_{t−p} − 1), where p is the number of periods per year. Works for every frequency; daily data are compared with the last observation on or before the same date a year earlier.

yoy(s1)

rebase(s, base_start, [base_end], [value]) · operation key rebase

Converts the values into an index: value · x_t / (average of x over the base period), e.g. 2015 = 100. The base can be a single period (2015, 2015-Q1) or a range from start to end.

rebase(s1, "2015")

rebase(s1, "2015", "", 100)

rebase(s1, "2019-Q1", "2019-Q4", 1)

trend(s, [method], [lam], [window]) · operation key trend

Estimates the trend of the series: a linear, quadratic or log-linear (exponential) time trend fitted by least squares, the Hodrick–Prescott filter (λ by frequency: annual 100, quarterly 1600, monthly 129 600) or a centred moving average (2×12 for monthly and 2×4 for quarterly data by default).

trend(s1, "hp")

trend(s1, "linear")

trend(s1, "moving_average", window=12)

cycle(s, [method], [lam], [low], [high], [k], [output]) · operation key cycle

Extracts the cyclical component: deviation from the Hodrick–Prescott trend, the Baxter–King or Christiano–Fitzgerald band-pass filter (cycles between the shortest and longest length, by default 1.5–8 years), the Hamilton (2018) regression filter (horizon h = 2 years, p = 1 year of lags) or the deviation from a linear trend. The '% deviation from trend' output gives the percentage deviation (computed on 100·ln x). Baxter–King leaves the first and last k observations empty (default k = 3 years), Hamilton the first h + p − 1. Band-pass and Hamilton filters need annual, semi-annual, quarterly or monthly data.

cycle(s1, "hp")

cycle(s1, "bk", low=1.5, high=8)

cycle(s1, "hamilton", output="pct")

sa(s, [method], [mode], [output]) · operation key seasonal_adjust

Removes seasonal effects from monthly or quarterly data. X-13ARIMA-SEATS (US Census Bureau: automatic ARIMA model, outlier detection, X-11 decomposition) is used when it is available on the server; otherwise, or when X-13 cannot adjust the series (it needs at least three full years), STL (seasonal-trend decomposition using LOESS) is used and the series history states this. 'Classical' is the ratio-to-moving-average method. Results: seasonally adjusted series, seasonal component, trend-cycle or irregular component. The multiplicative model suits positive series whose seasonal swings grow with the level; 'automatic' lets X-13 choose (STL and classical: multiplicative for positive series). At least two full years of data without gaps are required.

sa(s1, "x13")

sa(s1, "stl", "multiplicative")

sa(s1, "x13", output="seasonal")

hp(s, [lam], [output]) · operation key hp_filter

Hodrick–Prescott filter with smoothing parameter λ (empty = by frequency: annual 100, quarterly 1600, monthly 129 600). Returns the smooth trend or the cycle (series minus trend).

hp(s1)

hp(s1, 1600, "trend")

hp(s1, 1600, "cycle")

smooth(s, [method], [window], [alpha], [frac], [lam]) · operation key smooth

Smooths the series with one of several methods: moving average of the last n observations, centred moving average (2×n for even n), exponential smoothing (factor α, default 2/(n+1)), LOESS local regression (share of observations used in each fit, default 0.25), the Hodrick–Prescott filter (λ) or the Henderson moving average (n terms, odd; default 13 for monthly and 5 for quarterly data).

smooth(s1, "ma", 3)

smooth(s1, "centered_ma", 12)

smooth(s1, "ewma", alpha=0.3)

smooth(s1, "loess", frac=0.2)

smooth(s1, "henderson", 13)

abs(s) · operation key abs

Absolute value |x| of every value: negative values become positive.

abs(s1)

add(s, value) · operation key add

Adds a constant to every value: x + value. Series can also be added to each other in formulas (s1 + s2).

add(s1, 5)

s1 + 5

divide(s, value) · operation key divide

Divides every value by a non-zero constant: x / value.

divide(s1, 1000)

s1 / 1000

exp(s) · operation key exp

Exponential function eˣ – the inverse of the natural logarithm.

exp(log(s1))

log(s) · operation key log

Natural logarithm ln(x). Zero and negative values give empty results.

log(s1)

log10(s) · operation key log10

Base-10 logarithm log₁₀(x). Zero and negative values give empty results.

log10(s1)

multiply(s, value) · operation key multiply

Multiplies every value by a constant: x · value.

multiply(s1, 100)

s1 * 100

negate(s) · operation key negate

Changes the sign of every value: −x.

negate(s1)

power(s, value) · operation key power

Raises every value to a power: x^value. Results that are not real numbers (e.g. a fractional power of a negative value) are left empty.

power(s1, 2)

s1 ** 0.5

reciprocal(s) · operation key reciprocal

Reciprocal 1/x, e.g. to invert an exchange rate (EUR per USD → USD per EUR). Zero values give empty results.

reciprocal(s1)

round(s, [digits]) · operation key round

Rounds every value to the given number of decimal places; halves (e.g. 2.5) are rounded away from zero, as in Excel. A negative number of places rounds to tens, hundreds, … (−2 → nearest 100).

round(s1, 1)

scale(s, factor, [unit]) · operation key scale

Multiplies the series by a factor to change its unit, e.g. 0.001 converts millions to billions. Optionally sets the name of the new unit.

scale(s1, 0.001, "EUR billion")

scale(s1, 100)

sqrt(s) · operation key sqrt

Square root √x. Negative values give empty results.

sqrt(s1)

subtract(s, value) · operation key subtract

Subtracts a constant from every value: x − value.

subtract(s1, 2)

s1 - 2

annualize(s, [kind]) · operation key annualize

Expresses period values as annual rates: 'multiply' multiplies by the number of periods per year (e.g. a quarterly flow × 4, as in seasonally adjusted annual rates); 'compound' compounds a percentage growth rate over a year: 100·((1 + x/100)^p − 1).

annualize(s1)

annualize(qoq(s1), "compound")

fill(s, [method], [limit]) · operation key fill

Fills gaps inside the series by linear interpolation, with the previous value, the next value or zero. 'Maximum consecutive values' limits how many missing values in a row are filled. No values are created before the first or after the last observation. For daily data this also fills non-trading days (weekends, holidays).

fill(s1, "linear")

fill(s1, "ffill", 2)

S("key")

Loads any series from the MacroLens database by its key. The key is shown on the series page and in the search results; it must be written in quotes.

S("ESTAT/namq_10_gdp/Q.CLV10_MEUR.SCA.B1GQ.LT")

yoy(S("ESTAT/namq_10_gdp/Q.CLV10_MEUR.SCA.B1GQ.LT"))

U("code")

Loads a series that you saved in your library (or that was shared with you) by its code, written in quotes.

U("my_series")

U("my_series") / S("ESTAT/namq_10_gdp/Q.CLV10_MEUR.SCA.B1GQ.LT")

a + b

Adds series or numbers. Series are matched period by period; if a value is missing in either series, the result for that period is missing too.

s1 + s2

s1 + 100

a - b

Subtracts series or numbers, period by period.

s1 - s2

s1 - lag(s1, 1)

a * b

Multiplies series or numbers, period by period.

s1 * 1000

s1 * s2

a / b

Divides series or numbers, period by period. Division by zero gives a missing value.

s1 / s2 * 100

s1 / 1000

a ** b

Raises to a power. The ^ sign can be used instead of **.

s1 ** 2

(s1 / lag(s1, 4)) ^ 0.25

-a

Changes the sign of a series or number.

-s1

(a + b) * c

Group parts of a formula. Order of operations: powers first, then multiplication and division, then addition and subtraction. Series combined with operators must have the same frequency; use convert() otherwise.

(s1 + s2) / 2

if_missing(s, value)

Replaces the missing observations of a series with a number or with the values of another series of the same frequency for the same periods.

if_missing(s1, 0)

if_missing(s1, s2)

pi

The number π (3.14159…).

s1 * pi

e

Euler's number e (2.71828…), the base of the natural logarithm.

e ** (s1 / 100)

Pearson, Spearman or Kendall correlation matrix of two or more series over their common periods, with p-values, number of observations and 95% confidence intervals (Pearson).

Select two or more series of the same frequency.

How to read the results — in the user guide →

Correlation between series X shifted by k periods and series Y, for k = −K…K: shows which series leads and by how many periods.

Select exactly two series of the same frequency: first X, then Y.

How to read the results — in the user guide →

Number of observations, mean, standard deviation (sample and population), variance, coefficient of variation, minimum, maximum, quartiles, median, skewness, kurtosis, Jarque–Bera normality test, first and last period of each series.

Select one or more series.

How to read the results — in the user guide →

Simple (one explanatory variable) or multiple linear regression estimated by ordinary least squares: coefficients with standard errors, t-statistics, p-values and 95% confidence intervals, R², adjusted R², F-test, Durbin–Watson statistic, AIC, BIC, residual diagnostics, fitted values and residuals.

The first series is the dependent variable; the following series are the explanatory variables (one for a simple regression, several for a multiple regression).

How to read the results — in the user guide →

VAR model of two or more series: lag order selection (AIC, BIC, HQIC, FPE), coefficients of every equation, stability, Granger causality tests, impulse responses, forecast error variance decomposition and forecasts.

Select two to eight series of the same frequency. Their order matters for the orthogonalised impulse responses (Cholesky ordering).

How to read the results — in the user guide →

Principal components of two or more series over their common periods (standardised data by default): eigenvalues, share of explained variance, loadings and component series.

Select two or more series of the same frequency.

How to read the results — in the user guide →

Augmented Dickey–Fuller (ADF), Phillips–Perron (PP) and KPSS stationarity tests: test statistics, p-values, critical values and a plain-language conclusion.

Select one or more series; each is tested separately.

How to read the results — in the user guide →

Compares two or more periods of the same series side by side: number of observations, mean, median, standard deviation, minimum, maximum, total change and average annual growth rate.

Select one series and enter the periods to compare.

How to read the results — in the user guide →