# Custom likelihood with stochastic volatility

**URL:** <https://discourse.pymc.io/t/custom-likelihood-with-stochastic-volatility/8031>\
**Category:** Questions\
**Created:** [September 15, 2021, 8:18pm UTC](https://discourse.pymc.io/t/custom-likelihood-with-stochastic-volatility/8031 "2021-09-15T20:18:48Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![GMCobraz\_T](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/gmcobraz_t/32/4165_2.png) [@GMCobraz\_T](https://discourse.pymc.io/u/GMCobraz_T)\
**Post date:** [September 15, 2021, 8:18pm UTC](https://discourse.pymc.io/t/custom-likelihood-with-stochastic-volatility/8031/1 "2021-09-15T20:18:48Z")

</div>

Dear all,

I faced some error during sample posterior predictive.  
The error that I faced is as follow:  
ValueError: Distribution was not passed any random method. Define a custom random method and pass it as kwarg random

Below is my code:

import numpy as np  
import pandas as pd  
import datetime as dt  
from pandas\_datareader import data  
import matplotlib.pyplot as plt  
%matplotlib inline

np.random.seed(1000000) #Who wants to be a millionaire

start, end = dt.datetime(2014, 1, 1), dt.datetime(2015, 12, 31)  
sp500 = data.DataReader(’^GSPC’,‘yahoo’, start, end).loc[:,‘Close’]

#train, test = np.arange(0, 450), np.arange(451,509)

returns = np.log(sp500[1:] / sp500[0:-1].values) # Calculate log returns  
n=len(returns)-1  
plt.plot(returns)

import pymc3 as pm  
with pm.Model() as model:

```
y_obs_last = pm.Data('y_obs_last', returns[1:])

def custom_likelihood(y_obs_last, y_obs):
    expected = y_obs_last + corr
    return pm.StudentT.dist(nu=nu, mu=expected, lam=1/np.exp(-2*corr)).logp(y_obs)

sigma = pm.Exponential('sigma', 1./.02, testval=.1)
mu = pm.Normal('mu', 0, sd=5, testval=.1)

nu = pm.Exponential('nu', 1./10)
corr = pm.GaussianRandomWalk('corr', tau=sigma**-2, shape=n)

r = pm.DensityDist('r', custom_likelihood, observed={'y_obs_last': returns[1:], 'y_obs': returns[:-1]}) 

```

with model:  
start = pm.find\_MAP(vars=[corr], method=“L-BFGS-B”)

with model:  
step = pm.NUTS(vars=[corr, mu, nu,sigma],scaling=start, gamma=.25)  
start2 = pm.sample(100, step, start=start)[-1]

```
# Start next run at the last sampled position.
step = pm.NUTS(vars=[corr, mu, nu,sigma],scaling=start2, gamma=.55)
trace = pm.sample(2000, step, start=start2)

```

with model:  
y\_test = pm.sample\_posterior\_predictive(trace, 500)

May I know how to solve this error?  
Thanks in advance