How to incorporate a diagonal noise covariance matrix in statsmodel unobserved components?

[Roland K]

I frequently encounter data with time-varying a-priori noise standard deviations. I would like to preserve the ratio of the observation noise standard deviations and only estimate a joint scale factor as one of the SSM parameters. As far as I know I can't do this in the existing SSMs available in statsmodel - unobserved components. Can I do that in a custom state space model and if so, how does the implementation look like (e.g., for the local level model)?

[Chad Fulton]

Hello,

Yes, you can do this in a custom state space model.  If I understand correctly, you want a model like:

where s_t is known?

Then that would look like:

class CustomLocalLevel(sm.tsa.statespace.MLEModel):
    def __init__(self, endog, s_t):
        super().__init__(endog, k_states=1)

        self.s_t = np.array(s_t).reshape(1, 1, self.nobs)

        self['design', 0, 0] = 1.
        self['transition', 0, 0] = 1.
        self['selection', 0, 0] = 1.

        self.ssm.initialize_diffuse()

    @property
    def param_names(self):
        return ['sigma_eps', 'sigma_eta']

    @property
    def start_params(self):
        var = np.var(np.diff(self.endog[:, 0]))
        return np.r_[var / 3, 2 * var / 3]

    def transform_params(self, params):
        return params**2

    def untransform_params(self, params):
        return params**0.5

    def update(self, params, **kwargs):
        params = super().update(params, **kwargs)

        self['obs_cov'] = params[0] * self.s_t
        self['state_cov', 0, 0] = params[1]

Best,

Chad

On Fri, Sep 1, 2023 at 8:35 AM Roland K <rkle...@gmail.com> wrote:

I frequently encounter data with time-varying a-priori noise standard deviations. I would like to preserve the ratio of the observation noise standard deviations and only estimate a joint scale factor as one of the SSM parameters. As far as I know I can't do this in the existing SSMs available in statsmodel - unobserved components. Can I do that in a custom state space model and if so, how does the implementation look like (e.g., for the local level model)?

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[Roland K]

Thanks a lot. Exactly what I was looking for.

Op zondag 3 september 2023 om 19:03:26 UTC+2 schreef chadf...@gmail.com: