Simple moving average sma in python using numpy convolve

### simple moving average (sma) in python using numpy's `convolve`

the simple moving average (sma) is a commonly used indicator in time series analysis, particularly in finance. it calculates the average of a dataset over a specified number of periods, which helps to smooth out fluctuations and identify trends over time.

#### concept of sma

the sma is calculated by taking the arithmetic mean of a given set of values over a specified number of periods (often referred to as the window size). for example, if we have a dataset of daily stock prices and we want to calculate the 5-day sma, we would take the average of the stock prices for the last 5 days.

#### using numpy's `convolve`

numpy provides an efficient way to calculate the sma using the `convolve` function, which can be used to perform convolution operations. the sma can be computed by convolving the input data with a window of ones (of length equal to the number of periods) and then dividing by the number of periods.

### step-by-step tutorial

1. **import the required libraries**
2. **define the sma function**
3. **generate example data**
4. **compute the sma**
5. **visualize the results**

### implementation

here's how you can implement sma using numpy `convolve`:

### explanation of the code

2. **define the sma function**:
- we create a function `simple_moving_average` that takes the data and the window size as inputs.
- we generate weights for the moving average by creating an array of ones, dividing by the window size to ensure that the average is correctly calculated.

3. **generate example data**:
- we simulate stock prices using a cumulative sum of random values, centered around 100 for realistic stock price behavior.

4. **calculate the sma**: we ...

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