MinimalCausalContextBivarLinSVAR

Seed 1

Given are variables X_0 and X_1, where X_0 is a covariate and X_1 is the variable to forecast. Variables are generated from a linear Structural Vector Autoregressive (SVAR) model with additive gauss noise and a noise scale of 5.533e-04, with lag = 3.

The task is to forecast the value of the variable X_1 at time t, given the values of the covariate X_0 and the variable X_1 itself at times t-1, ... t-3.
For the first 128 days, the covariate X_0 takes a value of 8 from 2023-11-28 to 2024-01-13, 20 from 2024-01-14 to 2024-02-29, 8 from 2024-03-01 to 2024-04-03.
For the next 32 days, the covariate X_0 takes a value of 10 from 2024-04-04 to 2024-04-19, 20 from 2024-04-20 to 2024-04-21, 24 from 2024-04-22 to 2024-05-05. Each day can be treated as a timestep for the forecasting task. The causal parents affect the child variables at different lags.
The complete set of causal parents for each variable is given below, and there are no confounders.
No parents for X_0 at any lag.
Parents for variable X_1 at lag 1: X_0, X_1.
Parents for variable X_1 at lag 2: X_0, X_1.
Parents for variable X_1 at lag 3: X_0, X_1.

Types of context: ['Covariate information', 'Causal information']

Capabilities: ['Reasoning: Math', 'Reasoning: Causal', 'Retrieval: Memory']


Figure

Seed 2

Given are variables X_0 and X_1, where X_0 is a covariate and X_1 is the variable to forecast. Variables are generated from a linear Structural Vector Autoregressive (SVAR) model with additive gauss noise and a noise scale of 5.127e-04, with lag = 3.

The task is to forecast the value of the variable X_1 at time t, given the values of the covariate X_0 and the variable X_1 itself at times t-1, ... t-3.
For the first 128 days, the covariate X_0 takes a value of 2 from 2027-12-17 to 2027-12-18, 12 from 2027-12-19 to 2028-02-07, 2 from 2028-02-08 to 2028-03-26, 12 from 2028-03-27 to 2028-04-22.
For the next 32 days, the covariate X_0 takes a value of 40 from 2028-04-23 to 2028-05-05, 30 from 2028-05-06 to 2028-05-08, 60 from 2028-05-09 to 2028-05-17, 20 from 2028-05-18 to 2028-05-24. Each day can be treated as a timestep for the forecasting task. The causal parents affect the child variables at different lags.
The complete set of causal parents for each variable is given below, and there are no confounders.
No parents for X_0 at any lag.
Parents for variable X_1 at lag 1: X_0, X_1.
Parents for variable X_1 at lag 2: X_0, X_1.
Parents for variable X_1 at lag 3: X_0, X_1.

Types of context: ['Covariate information', 'Causal information']

Capabilities: ['Reasoning: Math', 'Reasoning: Causal', 'Retrieval: Memory']


Figure

Seed 3

Given are variables X_0 and X_1, where X_0 is a covariate and X_1 is the variable to forecast. Variables are generated from a linear Structural Vector Autoregressive (SVAR) model with additive gauss noise and a noise scale of 4.700e-04, with lag = 3.

The task is to forecast the value of the variable X_1 at time t, given the values of the covariate X_0 and the variable X_1 itself at times t-1, ... t-3.
For the first 128 days, the covariate X_0 takes a value of 12 from 2026-03-14 to 2026-04-12, 20 from 2026-04-13 to 2026-06-10, 12 from 2026-06-11 to 2026-07-19.
For the next 32 days, the covariate X_0 takes a value of 40 from 2026-07-20 to 2026-08-04, 80 from 2026-08-05 to 2026-08-04, 60 from 2026-08-05 to 2026-08-17, 20 from 2026-08-18 to 2026-08-20. Each day can be treated as a timestep for the forecasting task. The causal parents affect the child variables at different lags.
The complete set of causal parents for each variable is given below, and there are no confounders.
No parents for X_0 at any lag.
Parents for variable X_1 at lag 1: X_0, X_1.
Parents for variable X_1 at lag 2: X_0, X_1.
Parents for variable X_1 at lag 3: X_0, X_1.

Types of context: ['Covariate information', 'Causal information']

Capabilities: ['Reasoning: Math', 'Reasoning: Causal', 'Retrieval: Memory']


Figure

Seed 4

Given are variables X_0 and X_1, where X_0 is a covariate and X_1 is the variable to forecast. Variables are generated from a linear Structural Vector Autoregressive (SVAR) model with additive gauss noise and a noise scale of 1.487e-03, with lag = 3.

The task is to forecast the value of the variable X_1 at time t, given the values of the covariate X_0 and the variable X_1 itself at times t-1, ... t-3.
For the first 128 days, the covariate X_0 takes a value of 8 from 2024-02-21 to 2024-03-11, 12 from 2024-03-12 to 2024-05-06, 12 from 2024-05-07 to 2024-06-27.
For the next 32 days, the covariate X_0 takes a value of 30 from 2024-06-28 to 2024-07-13, 60 from 2024-07-14 to 2024-07-14, 60 from 2024-07-15 to 2024-07-29. Each day can be treated as a timestep for the forecasting task. The causal parents affect the child variables at different lags.
The complete set of causal parents for each variable is given below, and there are no confounders.
No parents for X_0 at any lag.
Parents for variable X_1 at lag 1: X_0, X_1.
Parents for variable X_1 at lag 2: X_0, X_1.
Parents for variable X_1 at lag 3: X_0, X_1.

Types of context: ['Covariate information', 'Causal information']

Capabilities: ['Reasoning: Math', 'Reasoning: Causal', 'Retrieval: Memory']


Figure

Seed 5

Given are variables X_0 and X_1, where X_0 is a covariate and X_1 is the variable to forecast. Variables are generated from a linear Structural Vector Autoregressive (SVAR) model with additive gauss noise and a noise scale of 2.782e-04, with lag = 3.

The task is to forecast the value of the variable X_1 at time t, given the values of the covariate X_0 and the variable X_1 itself at times t-1, ... t-3.
For the first 128 days, the covariate X_0 takes a value of 8 from 2027-03-05 to 2027-03-20, 2 from 2027-03-21 to 2027-04-29, 2 from 2027-04-30 to 2027-06-22, 2 from 2027-06-23 to 2027-07-10.
For the next 32 days, the covariate X_0 takes a value of 10 from 2027-07-11 to 2027-07-25, 40 from 2027-07-26 to 2027-07-26, 80 from 2027-07-27 to 2027-08-11. Each day can be treated as a timestep for the forecasting task. The causal parents affect the child variables at different lags.
The complete set of causal parents for each variable is given below, and there are no confounders.
No parents for X_0 at any lag.
Parents for variable X_1 at lag 1: X_0, X_1.
Parents for variable X_1 at lag 2: X_0, X_1.
Parents for variable X_1 at lag 3: X_0, X_1.

Types of context: ['Covariate information', 'Causal information']

Capabilities: ['Reasoning: Math', 'Reasoning: Causal', 'Retrieval: Memory']


Figure