Hi,

I’m trying to implement a simple exponential smoothing model (https://en.wikipedia.org/wiki/Exponential_smoothing). For those who aren’t familiar, this is a recursive model for sequences like time series that says yhat_t+1 = alpha * (x_t) + (1 - alpha) * (yhat_{t-1}), where alpha is a parameter and x the data.

Here is the code I’m using:

```
class Holt_Winters:
def __init__(self, freq, seasonal_period):
self.seasonal_period = seasonal_period
self.freq = freq
def fit(self, X, y):
pyro.clear_param_store()
nuts_kernel = NUTS(self.model)
posterior = MCMC(nuts_kernel, num_samples=4000, warmup_steps=1000).run(X, y)
post_summary = summary(posterior, sites=['yhat_initial', 'alpha'])
return post_summary
def predict(self, X):
pass
def model(self, X, y):
alpha = pyro.sample('alpha', Normal(0, 1))
yhat_prev = pyro.sample('yhat_initial', Normal(0, 1))
start = X.index.min() + pd.Timedelta(1, self.freq)
for d_1 in y[start:].index:
d = d_1 - pd.Timedelta(1, self.freq)
y_t = torch.tensor(X[d])
yhat_t_1 = alpha * y_t + (1 - alpha) * yhat_prev
y_t_1 = torch.tensor(y.loc[d_1])
sigma = pyro.sample(f'sigma_{d}', Normal(0, 1))
pyro.sample(f"yhat_{d_1} | {d}", Normal(yhat_t_1, sigma), obs=y_t_1)
yhat_prev = yhat_t_1
return alpha, yhat_prev
indent preformatted text by 4 spaces
```

For some reason, it is not fitting reasonable values on dummy data.

Dummy data:

```
dummy_df = pd.DataFrame(
{'x': np.arange(1, 5),
'y': np.arange(2, 6)
},
index=pd.date_range(start='1/1/2018', end='1/4/2018')
)
r = m.fit(dummy_df.x, dummy_df.y)
```

Can anyone spot an error in my code?

For reference, the most recent run I made, it fit a value of 2 for the initial and -1 for the alpha parameter, when clearly alpha should be 1 (always guess the most recent).