Hi,

I’m trying to fit a State Space Model with (stochastic) weekly seasonality and a linear local trend.

The transition equation for the hidden state is given by `theta_t=G @ theta_t-1 + w_t`

with G specified as below and `w_t,i ~ N(0, sigma_w_i)`

for i=1,2,3 and` w_t,i = 0`

for i>3.

```
G = [1, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, -1, -1, -1, -1, -1, -1],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0]
```

I’ve used a `Gamma(1,0.5)`

prior for all `sigma_w_i`

i=1,…,8 but this often results in a non-psd covariance matrix.

What is the best way to specify a transition distribution for a `GaussianHMM`

?

Should I use a different prior? Or is there a better way?

Kind regards

beta21