What is x13_auto_arima-Platform For AI(PAI)-阿里云帮助中心

x13_auto_arima is an algorithm for time series analysis that automatically selects an Autoregressive Integrated Moving Average (ARIMA) model. The algorithm is based on the procedure implemented by Gomez and Maravall (1998) in TRAMO (1996) and its subsequent revisions. It automatically identifies and selects the optimal ARIMA parameters to account for the seasonal and trend characteristics of the data. This automated process simplifies model building and improves prediction accuracy and efficiency.

Algorithm description

The x13_auto_arima component selects a model as follows:

Default model estimation
If frequency = 1, the default model is (0,1,1).
If frequency > 1, the default model is (0,1,1)(0,1,1).
Identification of differencing orders
If you set the diff and seasonalDiff parameters, this step is skipped.
You can use unit root tests to determine the difference d and the seasonal difference D.
Identification of ARMA model orders
The most appropriate model is selected based on the Bayesian information criterion (BIC). The maxOrder and maxSeasonalOrder parameters are used in this step.
Comparison of the identified model with the default model
The Ljung-Box Q statistic is used to compare the models. If both models are unacceptable, the (3,d,1)(0,D,1) model is used.
Final model checks

For more information about ARIMA, see Wikipedia. The algorithm has the following limits on the data scale:

Supported scales
- Rows: A maximum of 1,200 records per group.
- Columns: One numeric column.
Resource calculation method
- If groupColNames is not set, the default calculation method applies.
```
coreNum=1
memSizePerCore=4096
```
- Configuring groupColNames and the default calculation method
```
coreNum=floor(Total number of rows/120000)
memSizePerCore=4096
```

Limits

MaxCompute is the supported compute engine.

Component configuration

Method 1: Use the Designer UI

In your Designer workflow, add the x13_auto_arima component and configure its parameters in the pane that appears on the right.

Parameter type	Parameter	Description
Field settings	Time series	Required. This column is used only to sort the value column. The specific values are not used in calculations.
	Value column	Required.
	Group column	Optional. The group columns. To specify multiple columns, separate them with commas (,), for example, col0,col1. A time series is created for each group.
Parameter settings	Start date	The supported format is year.seasonal. Example: 1986.1.
	Series frequency	The value must be a positive integer in the range of (0, 12].
	Maximum p and q	The value must be a positive integer in the range of (0, 4].
	Maximum seasonal p and q	The value must be a number in the range of (0, 2].
	Maximum difference d	The value must be a positive integer in the range of (0, 2].
	Maximum seasonal difference d	You can enter a number in the range (0, 1].
	Difference d	The value must be a positive integer in the range of (0, 2]. If you set both the diff and maxDiff parameters, the maxDiff parameter is ignored. You must set the diff and seasonalDiff parameters together.
	Seasonal difference d	Enter a value in the range (0, 1]. If you set both the seasonalDiff and maxSeasonalDiff parameters, the maxSeasonalDiff parameter is ignored.
	Number of predictions	The number of entries to predict. For example, if you use the daily sales data of the last month to predict the sales for the next week, set this parameter to 7. If you specify group columns, this number of entries is predicted for each group. The value must be a positive integer in the range of (0, 120].
	Prediction confidence interval	The default value is 0.95.
	Tolerance	Optional. The default value is 1e-5.
	Maximum iterations	The value must be a positive integer. The default value is 1500.
Execution tuning	Number of cores	The number of workers. By default, the system automatically calculates this value.
Execution tuning	Memory size	The amount of memory per worker in MB.

Method 2: Use a PAI command

You can use a PAI command to configure the parameters of the x13_auto_arima component. You can use the SQL script component to run PAI commands. 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	Required	Default value	Description
inputTableName	Yes	None	The name of the input table.
inputTablePartitions	No	All partitions are used by default.	The feature columns in the input table to use for training.
seqColName	Yes	None	The time series column. This column is used only to sort the valueColName column.
valueColName	Yes	None	The value column.
groupColNames	No	None	The group columns. To specify multiple columns, separate them with commas (,), such as "col0,col1". A time series is created for each group.
start	No	1.1	The start date of the time series. The value must be a string in the `year.seasonal` format, such as `1986.1`. For more information, see Time series format.
frequency	No	12 Note A value of 12 indicates 12 months per year.	The frequency of the time series. The value must be a positive integer in the range of (0, 12]. For more information, see Time series format.
maxOrder	No	2	The maximum values of p and q. The value must be a positive integer in the range of [0, 4].
maxSeasonalOrder	No	1	The maximum values for the seasonal parameters p and q are integers in the range [0,2].
maxDiff	No	2	The maximum value of difference d. The value must be a positive integer in the range of [0, 2].
maxSeasonalDiff	No	1	The maximum value of the seasonal difference d, which must be an integer in the range [0,1].
diff	No	-1 Note A value of -1 indicates that diff is not specified.	The difference d. The value must be a positive integer in the range of [0, 2]. If you set both the diff and maxDiff parameters, the maxDiff parameter is ignored. You must set the diff and seasonalDiff parameters together.
seasonalDiff	No	-1 Note A value of -1 indicates that seasonalDiff is not specified.	The seasonal difference d. The value must be a positive integer in the range of [0, 1]. If you set both the seasonalDiff and maxSeasonalDiff parameters, the maxSeasonalDiff parameter is ignored.
maxiter	No	1500	The maximum number of iterations. The value must be a positive integer.
tol	No	1e-5	The tolerance. The value must be of the DOUBLE type.
predictStep	No	12	The number of prediction entries. The value must be a number in the range of (0, 365].
confidenceLevel	No	0.95	The prediction confidence level. The value must be a number in the range of (0, 1).
outputPredictTableName	Yes	None	The prediction output table.
outputDetailTableName	Yes	None	The table that contains the detailed information.
outputTablePartition	No	The output is not written to a partition by default.	The output partition. Specify the partition name.
coreNum	No	Automatically calculated by default.	The number of workers. This parameter is used with the memSizePerCore parameter. The value must be a positive integer.
memSizePerCore	No	Automatically calculated by default.	The memory size of each worker, in MB. The value must be a positive integer in the range of [1024, 64 × 1024].
lifecycle	No	By default, a lifecycle is not configured.	The lifecycle of the output table.

Time series format

The start and frequency parameters specify two time dimensions, ts1 and ts2, for the data in the value column:

frequency: The frequency of data within a unit period. This is the frequency of ts2 within each ts1.
start: The start date in the n1.n2 format. This indicates that the start date is the n2th ts2 in the n1th ts1.

Time unit	ts1	ts2	frequency	start
12 months/year	Year	Month	12	1949.2 indicates the second month of 1949.
Quarterly	Year	Quarter	4	1949.2 indicates the second quarter of 1949.
7 days/week	Week	Day	7	1949.2 indicates the second day of the 1949th week.
1	Any time unit	1	1	1949.1 indicates 1949 (year, day, or hour).

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

start=1949.3, frequency=12 indicates that the data is monthly (12 months per year) and the prediction starts from May 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 indicates that the data is quarterly (four quarters per year) and the prediction starts from the first quarter of 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 indicates that the data is recorded 7 days per week. The prediction starts from 1951.04.
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 indicates any time unit, and the prediction starts from 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 data

This example uses the AirPassengers.csv dataset, which contains the number of international airline passengers per month from 1949 to 1960. The following table shows a sample of the data. For more information about the dataset, see AirPassengers.

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

You can run the following Tunnel command on the MaxCompute client to upload the data. For more information about how to install and configure the MaxCompute client, see Connect to MaxCompute using the 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 the PAI command

You can use the SQL Script component or the ODPS SQL component to run the following PAI command.

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 description:

Output table: outputPredictTableName

Field description

column name	comment
pdate	The prediction date.
forecast	The prediction result.
lower	The lower bound of the prediction result at the specified confidence level. The default confidence level is 0.95.
upper	The upper bound of the prediction result at the specified confidence level. The default confidence level is 0.95.

Displaying data

Output table: outputDetailTableName
- Description
  column name
  comment
  key
  model: The model.
  evaluation: The evaluation result.
  parameters: The training parameters.
  log: The training log.
  summary
  Stores the specified information.
- Data view

FAQ

Why are all prediction results the same?
If an exception occurs during model training, the system defaults to the mean model. In this case, all prediction results are the mean of the training data. Common exceptions include instability after time series differencing, training that does not converge, and a variance of 0. You can view the stderr file of an individual node in Logview to find specific exception information.
How do I configure the component parameters?
You need to set parameters such as p, d, q, sp, sd, and sq for the x13_arima component. If you are unsure how to configure them, we recommend that you use
The x13_auto_arima component automatically searches for the optimal parameters. You only need to set an upper bound.
Error message: 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
This error occurs because there is not enough data. You can adjust the frequency or add more data.
Error message: ERROR: Order of the MA operator is too large
This error occurs because there is not enough data.
Error message: ERROR: Series to be modelled and/or seasonally adjusted must have at least 3 complete years of data
If you specify seasonal parameters, at least three years of data is required.

References

The x13_arima component provides an ARIMA algorithm for seasonal adjustment and is based on the open-source X-13ARIMA-SEATS. You can use this component to process data. For more information, see x13_auto_arima.

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

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

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

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

column name	comment
key	model: The model. evaluation: The evaluation result. parameters: The training parameters. log: The training log.
summary	Stores the specified information.