public/subjects/ai/time-series/audit/README.md

Exercise 0: Environment and libraries

The exercise is validated if all questions of the exercise are validated.

Activate the virtual environment. If you used conda run conda activate your_env.

Run python --version.

Does it print Python 3.x? x >= 8

Do import jupyter, import numpy and import pandas run without any error?

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Exercise 1: Series

The exercise is validated if all questions of the exercise are validated.

For question 1, is the output as below? The best solution uses pd.date_range to generate the index and range to generate the integer series.

    2010-01-01       0
    2010-01-02       1
    2010-01-03       2
    2010-01-04       3
    2010-01-05       4
                ...
    2020-12-27    4013
    2020-12-28    4014
    2020-12-29    4015
    2020-12-30    4016
    2020-12-31    4017
    Freq: D, Name: integer_series, Length: 4018, dtype: int64

Is the output as below? If the NaN values have been dropped the solution is also accepted. The solution uses rolling().mean().

    2010-01-01       NaN
    2010-01-02       NaN
    2010-01-03       NaN
    2010-01-04       NaN
    2010-01-05       NaN
                ...
    2020-12-27    4010.0
    2020-12-28    4011.0
    2020-12-29    4012.0
    2020-12-30    4013.0
    2020-12-31    4014.0
    Freq: D, Name: integer_series, Length: 4018, dtype: float64

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Exercise 2: Financial data

The exercise is validated if all questions of the exercise are validated.

Have the missing values and data types been checked?

Have the string dates been converted to datetime type?

Have the dates been set as index?

Have info or/and describe been used to have a first look at the data?

For question 1, are the right columns inserted in Candlestick Plotly object? The Candlestick is based on Open, High, Low and Close columns. The index is Date (datetime).

For question 2, is the output of print(transformed_df.head().to_markdown()) as below and are there 482 months?

Date	Open	Close	Volume	High	Low
1980-12-31 00:00:00	0.136075	0.135903	1.34485e+09	0.161272	0.112723
1981-01-30 00:00:00	0.141768	0.141316	6.08989e+08	0.155134	0.126116
1981-02-27 00:00:00	0.118215	0.117892	3.21619e+08	0.128906	0.106027
1981-03-31 00:00:00	0.111328	0.110871	7.00717e+08	0.120536	0.09654
1981-04-30 00:00:00	0.121811	0.121545	5.36928e+08	0.131138	0.108259

To get this result there are two ways: resample and groupby. There are two key steps:

• Find how to affect the aggregation on the last business day of each month. This is already implemented in Pandas and the keyword that should be used either in resample parameter or in Grouper is BM.
• Choose the right aggregation function for each variable. The prices (Open, Close and Adjusted Close) should be aggregated by taking the mean. Low should be aggregated by taking the minimum because it represents the lower price of the day, so the lowest price on the month is the lowest price of the lowest prices on the day. The same logic applied to High, leads to use the maximum to aggregate the High. Volume should be aggregated using the sum because the monthly volume is equal to the sum of daily volume over the month.

For question 3, does it not involve a for loop and is the output as below?

The first way to do it is to compute the return without for loop is to use pct_change. And the second way to do it is to implement the formula given in the exercise in a vectorized way. To get the value at t-1 the data has to be shifted with shift.

    Date
    1980-12-12         NaN
    1980-12-15   -0.047823
    1980-12-16   -0.073063
    1980-12-17    0.019703
    1980-12-18    0.028992
                    ...
    2021-01-25    0.049824
    2021-01-26    0.003704
    2021-01-27   -0.001184
    2021-01-28   -0.027261
    2021-01-29   -0.026448
    Name: Open, Length: 10118, dtype: float64

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Exercise 3: Multi asset returns

Is the outputted DataFrame's shape (261, 5) without having used a for loop and the is the output the same as the one returned with this line of code? The DataFrame contains random data. Make sure the output and the one returned by this code is based on the same DataFrame.

    market_data.pivot_table(values="Price", index="Date", columns="Ticker").pct_change()

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Exercise 4: Backtest

The exercise is validated if all questions of the exercise are validated.

Have the missing values and data types been checked?

Have the string dates been converted to datetime type?

Have the dates been set as index?

Have info or/and describe been used to have a first look at the data?

My results can be reproduced using: np.random.seed = 2712. Given the versions of NumPy used I do not guaranty the reproducibility of the results - that is why I also explain the steps to get to the solution.

For question 1, is the return computed as Return(t) = (Price(t+1) - Price(t))/Price(t) and returns the following output? Note that if the index is not ordered in ascending order the future return computed is wrong.

        Date
        1980-12-12   -0.052170
        1980-12-15   -0.073403
        1980-12-16    0.024750
        1980-12-17    0.029000
        1980-12-18    0.061024
                        ...
        2021-01-25    0.001679
        2021-01-26   -0.007684
        2021-01-27   -0.034985
        2021-01-28   -0.037421
        2021-01-29         NaN
        Name: Daily_futur_returns, Length: 10118, dtype: float64

An example of solution is:

        def compute_futur_return(price):
        return (price.shift(-1) - price)/price

        compute_futur_return(df['Adj Close'])

For question 2, is the index of the Series the same as the index of the DataFrame? The data of the series can be generated using np.random.randint(0,2,len(df.index).

For question 3, is the Pnl computed as: signal * futur_return? Both series should have the same index.

The below result are obtained considering the random strategy with the with np.random.seed = 2712

    Date
    1980-12-12   -0.052170
    1980-12-15   -0.000000
    1980-12-16    0.024750
    1980-12-17    0.029000
    1980-12-18    0.061024
                    ...
    2021-01-25    0.001679
    2021-01-26   -0.007684
    2021-01-27   -0.000000
    2021-01-28   -0.037421
    2021-01-29         NaN
    Name: PnL, Length: 10119, dtype: float64

For question 4, is the return of the strategy computed as: (Total earned - Total invested) / Total invested? The result should be close to 0. The formula given could be simplified as (PnLs.sum())/signal.sum(). My return is: 0.00043546984088551553 because I invested 5147$ and I earned 5149$.

For question 5, is the previous signal Series being replaced with 1s? Similarly as the previous question, we earned 10128$ and we invested 10118$ which leads to a return of 0.00112670194140969 (0.1%).