• | Kalman filter algorithm: YADA supports four methods for computing the Kalman filter: the standard filter, the square-root filter, the univariate filter, and Chandrasekhar recursions. The first, third and the last are (potentially) fast, while the last three are robust, where the square-root filter guarantees that all covariance matrices are also numerically positive semidefinite. The Chandrasekhar recursions are the fastest when the number of state variables is sufficiently larger than the number of observed variables. They are only consistent with constant parameter models and in YADA they require that the model is covariance stationary (no unit roots and a constant mapping from the state variables to observed variables). |
• | Select method for initializing the state covariance matrix: YADA supports 4 methods for initializing the state covariance matrix for the forecasting part P1|0: (1) Analytically through vectorization; (2) Numerically through the doubling algorithm; (3) Constant times the identity; and (4) Diffuse initialization. |
• | Maximum number of iterations for the doubling algorithm: Lets you choose the maximum number of interations for the doubling algorithm. For k iterations, the doubling algorithm provides 2k -1 summations. Values between 100 and 2,000 are supported by the control. |
• | Tolerance level for the doubling algorithm: The convergence criterion for the doubling algorithm is the norm of the change in the value of the covariance matrix. The norm function in matlab is the largest singular value. |
• | Constant for initial state covariance matrix: This option lets you choose the constant in method 3 for initializing the forecast covariance matrix of the state vector. Values between 1 and 10,000 are possible. If a state variable is defined as a unit root process (see Actions menu), the forecast covariance term for that variable is initialized by this constant. |
• | First observation after Kalman filter training sample: Lets you set up a training sample for the Kalman filter. The training sample is defined as the first observation of the estimation sample (see Sample Selections) until the last period before to the period selected with this option. The training sample itself is used when computing the state variable estimates with the Kalman filter, but is skipped when calculating the log likelihood. |
• | Numerical tolerance for DSGE model solver: Lets you choose the numerical tolerance for the DSGE model solvers. This primarily affects how eigenvalues close to unity are treated. |
• | Use own initial values for the state variables: By default YADA initializes the state vector at zero, the unconditional mean of the state vector. You can set new initial values for the state vector ξ1|0 from the function Set Initial State Values on the Actions menu. Those value are used when the current control is check marked. |
• | Allow for undefined unit roots: The Kalman filter will automatically check for undefined unit roots in the state equation when this option is not check marked. If unit roots are found, the Kalman filter will provide a negative status and the function calling the filter will be abandoned. To avoid this type of behavior you can check mark the option. In that case, YADA will use method (3) for initializing the state covariance matrix if at least one unit root is found in the state equation. |

Additional Information
• | A more detailed description about the Kalman filter is found in Section 5 of the YADA Manual. |
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