# Simulating Exponential Moving Average with Python First, we need to have Jupyter Lab installed as well as the Jupyter extension. The file we'll work with is located under `notebook/curve_v2_ema.ipynb`. To start, let's start our Jupyter Server. In the terminal, we'll type: ```bash jupyter lab ``` The server logs will indicate what URL to use to access the server. Copy the URL and connect our code editor to the Jupyter Server by selecting `Select Kernel` > `Select Another Kernel` > `Existing Jupyter Server` and paste in the copied URL. Finally, click `connect`. Now we can select the version of python we want to use for our Jupyter session. Now that we're connected, let�s install the Python libraries we�ll need for this example. These libraries are called `numpy` and `matplotlib`. To do this we will enter the following into the code cell: ```python !pip install numpy !pip install matplotlib ``` Now that we have installed the necessary libraries, let�s write some code by clicking on the `+ Code` button to open up a new cell. Let's import the installed libraries: ```python import numpy as np import matplotlib.pyplot as plt ``` Next, we�ll define a function that will calculate the exponential moving average for regular intervals. We will call this function `ema`. This function will take two inputs: the current price, and the previous exponential moving average. We'll also define a variable `a` equal to `0.1`. Finally, we�ll return the exponential moving average. This all boils down to the following code: ```python def ema(p, u): a = 0.1 return a * p + (1 - a) * u ``` Now we are going to create 100 random points that represent the price of a token. ```python N = 100 ``` We'll set our initial price as 10: ```python p0 = 10 ``` Next, let�s create some random points that will represent the change in price: ```python v = 2 delta_prices = np.random.normal(0, v, N) ``` Then, let�s see what the delta prices looks like by printing them out: ```python delta_prices ``` We can see that these are a bunch of random numbers that deviate from 0. Next, let�s create an array of prices: ```python prices = [] ``` Then, we'll set the current price to `p0`: ```python p = p0 ``` Now let's run a for loop and add the delta price to the current price and store this in the prices array, but make sure that the price never goes below zero: ```python for dp in delta_prices: prices.append(p) p += dp if p < 0: p = 0 ``` Now, let's plot these prices by adding the following code: ```python plt.plot(prices) plt.show() ``` Finally, we�ll calculate and plot the exponential moving average on the same graph. First, create an array of the exponential moving averages: ```python emas = [] ``` Then initialize our exponential moving average variable `u` to the initial price: ```python u = p0 ``` Next let�s run a for loop and use our previously defined `ema` function to store and calculate the exponential moving average: ```python for p in prices: emas.append(u) u = ema(p, u) ``` Finally, let�s plot the exponential moving average on the same graph and add a legend to distinguish the two: ```python plt.plot(emas) plt.legend(["price", "ema"]) plt.show() ``` Finally, we can play around with the `a` parameter. For example, if instead of `0.1`, we set it to `0.9`. we see the exponential moving average changes to follow the price more closely.