The R package Mcomp contains the 1001 time series from the M-competition (Makridakis et al. 1982), the 3003 time series from the IJF-M3 competition (Makridakis and Hibon, 2000), and the forecasts contributed to the IJF-M3 competition. See also the tscompdata package for data from other forecasting competitions.

## M1 competition

The M1 forecasting competition was organized by Spyros Makridakis and Michèle Hibon, involving 1001 series. In this competition, anyone could submit forecasts, making this the first true forecasting competition as far as I am aware. They also used multiple forecast measures to determine the most accurate method.

The 1001 time series were taken from demography, industry and economics, and ranged in length between 9 and 132 observations. All the data were either non-seasonal (e.g., annual), quarterly or monthly. Curiously, all the data were positive, which made it possibly to compute mean absolute percentage errors, but was not really reflective of the population of real data.

The M1 competition data are stored as M1.

library(Mcomp)
M1
#> M-Competition data: 1001 time series
#>
#>            Type of data
#> Period      DEMOGR INDUST MACRO1 MACRO2 MICRO1 MICRO2 MICRO3 Total
#>   MONTHLY       75    183     64     92     10     89    104   617
#>   QUARTERLY     39     18     45     59      5     21     16   203
#>   YEARLY        30     35     30     29     16     29     12   181
#>   Total        144    236    139    180     31    139    132  1001

Functions are provided to plot and manage the date. The plot.Mdata() and autoplot.Mdata() functions plot a time series, showing both the training and test sections of the series.

plot(M1[[1]])

autoplot(M1[[1]])

subset.Mcomp() returns a subset of the time series data; subsets can be for specific periods, or specific types of data or both.

subset(M1, "monthly")
#> M-Competition data: 617 MONTHLY time series
#>
#>          Type of data
#> Period    DEMOGR INDUST MACRO1 MACRO2 MICRO1 MICRO2 MICRO3
#>   MONTHLY     75    183     64     92     10     89    104
subset(M1, "macro1")
#> M-Competition data: 139 MACRO1 time series
#>
#>            Type of data
#> Period      MACRO1
#>   MONTHLY       64
#>   QUARTERLY     45
#>   YEARLY        30
subset(M1, "macro1", "monthly")
#>          Type of data
#> Period    MACRO1
#>   MONTHLY     64

The 111 series used in the extended comparisons in the 1982 M-competition can also be selected.

subset(M1, 111)
#> M-Competition data: 111 time series
#>
#>            Type of data
#> Period      DEMOGR INDUST MACRO1 MACRO2 MICRO1 MICRO2 MICRO3 Total
#>   MONTHLY        8     21      8      9      1     10     11    68
#>   QUARTERLY      5      2      5      6      0      3      2    23
#>   YEARLY         3      4      4      3      2      3      1    20
#>   Total         16     27     17     18      3     16     14   111

M1 is of class Mcomp which is a list, where each element is also a list containing information about one time series. For example, the first element contains the following information.

str(M1[[1]])
#> List of 9
#>  $st : chr "Y1" #>$ n          : num 22
#>  $h : num 6 #>$ period     : chr "YEARLY"
#>  $type : chr "MICRO1" #>$ description: chr "FRANCE LA REGIE RENAULT A25 ANS(CHAMBRE DE COMMERCE FRANCAIS) TURNOVER-RENAULT"
#>  $x : Time-Series [1:22] from 1972 to 1993: 3600 7700 12300 30500 47390 ... #>$ xx         : Time-Series [1:6] from 1994 to 1999: 588568 646758 849998 1106740 1184550 ...
#>  \$ sn         : chr "YAF2"
#>  - attr(*, "class")= chr "Mdata"

The various items are as follows:

• st: the series number and period. For example Y1 denotes the first yearly series, Q20 denotes the 20th quarterly series, and so on;
• n: the number of observations in the training part of the time series;
• h: the number of required forecasts (equivalently the number of observations in the test part of the time series);
• period: interval of the time series. Possible values are YEARLY, QUARTERLY, MONTHLY & OTHER.
• type: the type of series. Possible values are DEMOGR, INDUST, MACRO1, MACRO2, MICRO1, MICRO2 & MICRO3.
• description: a short description of the time series;
• x: the training part of the time series of length n;
• xx: the test part of the time series of length h.
• sn: name of the series;

## M3 competition

In 1998, Makridakis & Hibon ran their M3 competition. Entrants had to forecast 3003 time series and the results were compared to a test set that was withheld from participants. The time series were all taken from business, demography, finance and economics, and ranging in length between 14 and 126 observations. Again, the data were all either non-seasonal (e.g., annual), quarterly or monthly, and all were positive.

The time series from the M3 forecasting competition and the forecasts from all the original participating methods are stored in M3 and M3Forecast respectively. plot.Mdata(), autoplot.Mdata() and subset.Mcomp() work on M3 as well. The structure of M3 is the same as for M1.

M3Forecast is a list of data.frames. Each list element is the result of one forecasting method. The data.frame then has the following structure. Each row is the forecast of one series; rows are named accordingly. Each column corresponds to a forecast horizon. There are 18 columns, as the maximum number of forecasts for any series is 18. If fewer forecasts than 18 exist, the row is padded with NA values.

M3
#> M-Competition data: 3003 time series
#>
#>            Type of data
#> Period      DEMOGRAPHIC FINANCE INDUSTRY MACRO MICRO OTHER Total
#>   MONTHLY           111     145      334   312   474    52  1428
#>   OTHER               0      29        0     0     4   141   174
#>   QUARTERLY          57      76       83   336   204     0   756
#>   YEARLY            245      58      102    83   146    11   645
#>   Total             413     308      519   731   828   204  3003
autoplot(M3[[1]])

subset(M3, "macro")
#> M-Competition data: 731 MACRO time series
#>
#>            Type of data
#> Period      MACRO
#>   MONTHLY     312
#>   QUARTERLY   336
#>   YEARLY       83