# Estimate correlation between two time series

**URL:** <https://discourse.julialang.org/t/estimate-correlation-between-two-time-series/58505>\
**Category:** Probabilistic Programming\
**Created:** [April 3, 2021, 2:29pm UTC](https://discourse.julialang.org/t/estimate-correlation-between-two-time-series/58505 "2021-04-03T14:29:31Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![stebett](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stebett/32/20336_2.png) [@stebett](https://discourse.julialang.org/u/stebett)\
**Post date:** [April 3, 2021, 2:29pm UTC](https://discourse.julialang.org/t/estimate-correlation-between-two-time-series/58505/1 "2021-04-03T14:29:31Z")

</div>

Hello, I’m a new Turing user and I’m not very familiar with probabilistic modeling, but the package is so cool that I couldn’t help trying to implement some of it 🙂

Basically I have 2 Bernoulli/Poisson processes (binned spike trains) and I’d like to know **if** and **how much** one influences the other.

So my data has this form:

```julia-auto
s₁ = [0, 0, 1, 0, 1]
s₂ = [1, 0, 0, 0, 1]

```

and I’ve computed a feature which is the delay of the closest spike of s₂

```julia-auto
x = [0, 1, 2, 1, 0]

```

Then I’ve built the model:

```julia-auto
@model my_naive_model(x, y, n, σ²) = begin
	b0 ~ Normal(0, σ²)
	b1 ~ Normal(0, σ²)
	for i = 1:n
		theta = b0 + b1*x[i, 1] 
		y[i] ~ Bernoulli(sigmoid(theta))
	end
end;

```

Trained it:

```julia-auto
chain = sample(my_naive_model(x, s₁, length(x), 10), NUTS(200, 0.65), 1500, discard_adapt=false)

```

And took the predictions with:

```julia-auto
function prediction(x::Vector, chain)
	p0 = mean(chain, :b0)
	p1 = mean(chain, :b1)
	r = zeros(size(x, 1))
	for i = 1:n
		theta = p0 + p1*x[i]
		r[i] = sigmoid(theta)
	end
	r
end;

```

And that was awesomely easy, but I’d like to do something a bit more complicated, so these are my questions:

### 1.

What could be a sensible transformation of x, or how could I figure this out?  
For example, I guess I could fit a polynomial, but what about embedding a smoothing spline or another non parametric regression method?

### 2.

How do I understand the magnitude of the effect that `s₂` has on `s₁`? In particular if I’m using a polynomial fit, how can I say that `s₂` is actually having an effect on `s₁`?

### 3.

This follows directly from the second question: Let’s say that I have a third spike train, and I want to `s₃`, and I want to prove that it has no effect at all on `s₁`. How do I do that?

Thank you very much in advance, and thanks to all Turing developers for the marvelous work!