MAD_m40: Hourly Traffic Volume on the M-40 Ring Road, Madrid

In msarima: Multi-Seasonal ARIMA Models

Hourly Traffic Volume on the M-40 Ring Road, Madrid

Description

Number of vehicles per hour recorded by a single traffic sensor on the M-40, the outer ring road of Madrid, over the eight weeks from 3 February to 29 March 2024.

The series shows the two seasonal patterns that msarima is meant for: a daily cycle of period 24, with the morning and evening commuting peaks, and a weekly cycle of period 168, with markedly lower volumes at the weekend.

Usage

MAD_m40

Format

An msts object of length 1344 (56 days, or eight complete weeks, of hourly data) with seasonal periods 24 and 168. The first observation is midnight of Saturday 3 February 2024 and the last is 11 p.m. of Friday 29 March 2024.

Details

The raw measurements are half-hourly counts from sensor 3753, recorded between 1 February and 31 May 2024 and summed in pairs to obtain hourly volumes; the eight weeks kept here are the window studied by Grigoletto and Lisi (2026), who chose this sensor for having the fewest missing observations in the network. A few of the underlying half-hourly counts had been interpolated by the provider, so 3 of the hourly values are not whole numbers. There are no missing values and no gaps in the hourly grid.

The script that builds the object from the raw file is available at https://github.com/danigiro/msarima/blob/main/data-raw/MAD_m40.R.

Source

Madrid City Council open data portal, https://datos.madrid.es.

References

Grigoletto, M. and Lisi, F. (2026). Portmanteau goodness-of-fit tests in the presence of simple, mixed, and multiple seasonal autocorrelation. arXiv. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2609.32381")}

Examples

# The daily and weekly cycles
plot(window(MAD_m40, end = 4), ylab = "vehicles per hour")

# A multi-seasonal ARIMA with one daily and one weekly difference

fit <- msarima(MAD_m40,
               order = c(1, 0, 2),
               seasonal = list(c(0, 1, 1), c(0, 1, 1)))
summary(fit)
plot(forecast(fit, h = 48))

msarima documentation built on Nov. 12, 2026, 5:11 p.m.