# Likelihood increases on increasing variance of measurement error in kalman filter

I tried to fit a local trend model to daily data of a currency. I used the "dlm" package and tried to estimate the parameters V (measurement noise) and W (the process noise) via maximum likelihood.

The outputted value of parameters didnt made any sense intuitively. So, I put the value of parameters which made sense to me (just variance of the (|moving average(5) - current| as V and Variance of Moving average(5) as W.

Then i used these values to estimate the likelihood of the model.(dlmFilter with model and data in R). The likelihood was greater than what mle previosly suggested.

However even after using these values as starting values of parameters the mle outputs unsensible parameters values with likelihood lingering around the same point. Also inspite of varying starting value of parameters for mle through plethora of values it never outputs a sensible value.(I also tried all the optimization techniques available).

1.Can anyone suggest what i am doing wrong(if any) and what to avoid during evaluating complex models ?

2.The backtest result of strategy are better for my parameters than the parameters puked by the mle. Which should i follow?

If i increase the values of V or W the likelihood of the model increases. I cant think of a mathematical reason for this to happen.

3.Should i drop likelihood and look for other things like normality of residuals,no auto-correlation among them as factors to judge models.

1. Any other suggestion would be welcomed.

Edit :

The simple local trend model :

$$X_t$$ = $$X_(t-1)$$ + $$w_t$$ w ~ N(0,W^2)

$$Y_t$$ = $$X_t$$ + $$v_t$$ v ~ N(0,V^2)

I was trying to estimate V and W (measurement and process noise variances) and m0 and C0 the initial distribution of the state vector.

• you should provide the equations for the DLM so that your question is more easily understood. – mark leeds Oct 19 '19 at 15:09