What is x13_auto_arima - Platform For AI - Alibaba Cloud Documentation Center

Automatically selects optimal ARIMA models for time series data using procedures from Gomez and Maravall (1998) and TRAMO (1996).

How it works

The component selects the best ARIMA model through four steps:

Default model estimation
- For frequency = 1, the default model is (0,1,1).
- For frequency > 1, the default model is (0,1,1)(0,1,1).
Differencing order identification: If diff and seasonalDiff are specified, this step is skipped. Otherwise, unit root tests determine the non-seasonal differencing order d and seasonal differencing order D.
ARMA order identification: Selects the most appropriate model based on Bayesian Information Criterion (BIC). maxOrder and maxSeasonalOrder parameters control upper bounds.
Model comparison and final checks: Ljung-Box Q statistic compares the identified model against the default model. If both models are unacceptable, falls back to (3,d,1)(0,D,1) model.

For more information about ARIMA, see Autoregressive integrated moving average.

Limitations

Runs only on MaxCompute computing resources.
Maximum 1,200 data records per group.
One numeric column.

Resource calculation

Without groupColNames:
```
  coreNum = 1
  memSizePerCore = 4096
```

With groupColNames:

  coreNum = floor(Total number of rows / 120,000)
  memSizePerCore = 4096

Configure the component

Configure x13_auto_arima in one of the following ways:

Method 1: Configure in the PAI console
Method 2: Configure with PAI commands

Method 1: Configure in the PAI console

Configure parameters on the pipeline page of Machine Learning Designer.

Fields Setting

Parameter	Required	Description
Time Series Column	Yes	Sorts values in the value column.
Value Column	Yes	Numeric column containing time series values.
Stratification Column	No	Separate multiple columns with commas (`,`), such as `col0,col1`. Creates a separate time series for each group.

Parameters Setting

Parameter	Description	Default
Start Date	Format: `year.seasonal`. Example: `1986.1`.	--
Series Frequency	Positive integer in the range (0,12].	--
Maximum of p and q	Positive integer in the range (0,4].	--
Maximum of Seasonal p and q	Number in the range (0,2].	--
Maximum of Difference d	Positive integer in the range (0,2].	--
Maximum of Seasonal Difference d	Positive integer in the range (0,1].	--
Difference d	Positive integer in the range (0,2]. If both `diff` and `maxDiff` are specified, `maxDiff` is ignored. Must be used with `seasonalDiff`.	--
Seasonal Difference d	Positive integer in the range (0,1]. If both `seasonalDiff` and `maxSeasonalDiff` are specified, `maxSeasonalDiff` is ignored.	--
Prediction Entries	Number of predictions. For example, to predict sales for the next 7 days based on the past month, set this to `7`. If Stratification Column is selected, each group produces this many predictions. Positive integer in the range (0,120].	--
Prediction Confidence Interval	Confidence level for calculating prediction intervals.	0.95
Tolerance	Optional. Convergence tolerance for model fitting.	1e-5
Maximum Iterations	Positive integer.	1500

Execution Tuning

Parameter	Description
Cores	Number of cores. System determines automatically by default.
Memory Size	Memory size per core, in MB.

Method 2: Configure with PAI commands

Run PAI commands through SQL scripts. For more information, see SQL Script.

PAI -name x13_auto_arima
    -project algo_public
    -DinputTableName=pai_ft_x13_arima_input
    -DseqColName=id
    -DvalueColName=number
    -Dstart=1949.1
    -Dfrequency=12
    -DpredictStep=12
    -DoutputPredictTableName=pai_ft_x13_arima_out_predict2
    -DoutputDetailTableName=pai_ft_x13_arima_out_detail2

Parameter reference

Parameter	Required	Description	Default
inputTableName	Yes	Name of the input table.	N/A
inputTablePartitions	No	Feature columns selected from the input table for model training.	Full table
seqColName	Yes	Time series column. Sorts values in the value column.	N/A
valueColName	Yes	Value column.	N/A
groupColNames	No	Stratification columns. Separate multiple columns with commas (`,`), such as `col0,col1`. Creates a separate time series for each group.	N/A
start	No	Start time of the time series. Format: `year.seasonal`, such as `1986.1`. For details, see Time series format.	1.1
frequency	No	Time series frequency. Positive integer in the range (0,12]. A value of 12 indicates 12 months (one year). For details, see Time series format.	12
maxOrder	No	Maximum values of p and q. Positive integer in the range [0,4].	2
maxSeasonalOrder	No	Maximum values of seasonal p and q. Positive integer in the range [0,2].	1
maxDiff	No	Maximum non-seasonal differencing order d. Positive integer in the range [0,2].	2
maxSeasonalDiff	No	Maximum seasonal differencing order d. Positive integer in the range [0,1].	1
diff	No	Non-seasonal differencing order d. Positive integer in the range [0,2]. If both `diff` and `maxDiff` are specified, `maxDiff` is ignored. Must be used with `seasonalDiff`. Value of -1 indicates unspecified differencing order.	-1
seasonalDiff	No	Seasonal differencing order d. Positive integer in the range [0,1]. If both `seasonalDiff` and `maxSeasonalDiff` are specified, `maxSeasonalDiff` is ignored. Value of -1 indicates unspecified seasonal differencing order.	-1
maxiter	No	Maximum number of iterations. Positive integer.	1500
tol	No	Convergence tolerance. DOUBLE type.	1e-5
predictStep	No	Number of prediction entries. Positive integer in the range (0,365].	12
confidenceLevel	No	Confidence level for prediction intervals. Number in the range (0,1).	0.95
outputPredictTableName	Yes	Output prediction table.	N/A
outputDetailTableName	Yes	Output details table.	N/A
outputTablePartition	No	Whether to export data to a partition.	Does not export data to partitions
coreNum	No	Number of cores. Positive integer. Used with `memSizePerCore`.	Determined by the system
memSizePerCore	No	Memory size per core, in MB. Positive integer in the range [1024, 65536].	Determined by the system
lifecycle	No	Lifecycle of the output table.	N/A

Time series format

start and frequency parameters define two time dimensions, ts1 and ts2, for the numeric column.

frequency specifies how many ts2 units fit within one ts1 unit.
start uses the format n1.n2, meaning the series starts at the n2th ts2 in the n1th ts1.

Common configurations:

Time unit	ts1	ts2	frequency	start example
12 months/year	Year	Month	12	`1949.2` = February 1949
4 quarters/year	Year	Quarter	4	`1949.2` = Q2 1949
7 days/week	Week	Day	7	`1949.2` = second day of the 1949th week
1	Any time unit	1	1	`1949.1` = the year 1949, or the 1949th day or hour

Time series examples

Given: value = [1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

start=1949.3, frequency=12 (monthly data, 12 months per year)

Prediction starts from June 1950.

year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1949			1	2	3	4	5	6	7	8	9	10
1950	11	12	13	14	15

start=1949.3, frequency=4 (quarterly data, 4 quarters per year)

Prediction starts from Q2 1953.

year	Qtr1	Qtr2	Qtr3	Qtr4
1949			1	2
1950	3	4	5	6
1951	7	8	9	10
1952	11	12	13	14
1953	15

start=1949.3, frequency=7 (daily data, 7 days per week)

Prediction starts from the fourth day of the 1951st week.

week	Sun	Mon	Tue	Wed	Thu	Fri	Sat
1949			1	2	3	4	5
1950	6	7	8	9	10	11	12
1951	13	14	15

start=1949.1, frequency=1 (non-seasonal data)

Prediction starts in 1963.

cycle	p1
1949	1
1950	2
1951	3
1952	4
1953	5
1954	6
1955	7
1956	8
1957	9
1958	10
1959	11
1960	12
1961	13
1962	14
1963	15

Examples

Prepare test data

This example uses the AirPassengers.csv dataset, which records the number of international airline passengers per month from 1949 to 1960. For more information about the dataset, see AirPassengers.

Sample data:

id	number
1	112
2	118
3	132
4	129
5	121
...	...

Run the following Tunnel commands on the MaxCompute client to upload data. For information about installing and configuring the MaxCompute client, see MaxCompute client (odpscmd). For more information about Tunnel commands, see Tunnel commands.

create table pai_ft_x13_arima_input(id bigint, number bigint);
tunnel upload xxx/airpassengers.csv pai_ft_x13_arima_input -h true;

Run PAI commands

Use the SQL script or ODPS SQL component to run PAI commands:

PAI -name x13_auto_arima
    -project algo_public
    -DinputTableName=pai_ft_x13_arima_input
    -DseqColName=id
    -DvalueColName=number
    -Dstart=1949.1
    -Dfrequency=12
    -DmaxOrder=4
    -DmaxSeasonalOrder=2
    -DmaxDiff=2
    -DmaxSeasonalDiff=1
    -DpredictStep=12
    -DoutputPredictTableName=pai_ft_x13_arima_auto_out_predict
    -DoutputDetailTableName=pai_ft_x13_arima_auto_out_detail

Output

Prediction table (outputPredictTableName)

Column	Description
pdate	Date of the prediction.
forecast	Prediction conclusion.
lower	Lower bound of the prediction interval at the specified confidence level. Default: 0.95.
upper	Upper bound of the prediction interval at the specified confidence level. Default: 0.95.

Generated data:

Prediction output

Details table (outputDetailTableName)

Column	Description
key	One of the following: `model` (the model in use), `evaluation` (the evaluation result), `parameters` (training parameters), or `log` (training logs).
summary	Storage details for the corresponding key.

Generated data:

Details output

FAQ

Why are all prediction results the same value?

This happens when the model training encounters an exception and falls back to the mean model, which outputs the mean of the training data for all predictions. Common causes include instability after differencing, failure to converge during training, or a variance of 0 in the input data.

To diagnose the specific error, check the stderr file of individual nodes in Logview.

How do I choose between x13_arima and x13_auto_arima?

x13_arima requires manually specifying the p, d, q, sp, sd, and sq parameters. If you are unsure which values to use, choose x13_auto_arima instead. With x13_auto_arima, set only upper bounds (such as maxOrder and maxDiff), and the component tunes parameters automatically.

Error: Number of observations after differencing is less than the minimum series length

ERROR: Number of observations after differencing and/or conditional AR estimation
is 9, which is less than the minimum series length required for the model estimated, 24

The training data is insufficient for the specified model. Modify the frequency parameter or add more training data.

Error: Order of the MA operator is too large

ERROR: Order of the MA operator is too large

This error typically indicates insufficient training data. Add more data points to your input table.

Error: Series must have at least 3 complete years of data

ERROR: Series to be modelled and/or seasonally adjusted must have at least 3 complete
years of data

When seasonal parameters are specified, the input data must contain at least three complete years of observations.

References

X-13ARIMA-SEATS is a seasonally adjusted autoregressive integrated moving average (ARIMA) model algorithm based on the open-source X-13ARIMA-SEATS algorithm. For the related manual-parameter component, see x13_arima.