from os.path import basename, exists


def download(url):
    filename = basename(url)
    if not exists(filename):
        from urllib.request import urlretrieve

        local, _ = urlretrieve(url, filename)
        print("Downloaded " + local)


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkstats2.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkplot.py")

import numpy as np
import pandas as pd

import random

import thinkstats2
import thinkplot

"""
Explanation: Chapter 12
Examples and Exercises from Think Stats, 2nd Edition
http://thinkstats2.com
Copyright 2016 Allen B. Downey
MIT License: https://opensource.org/licenses/MIT
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/mj-clean.csv")

transactions = pd.read_csv("mj-clean.csv", parse_dates=[5])
transactions.head()

"""
Explanation: Time series analysis
NOTE: Some of the example in this chapter have been updated to work with more recent versions of the libraries.
Load the data from "Price of Weed".
End of explanation
"""


def GroupByDay(transactions, func=np.mean):
    """Groups transactions by day and compute the daily mean ppg.

    transactions: DataFrame of transactions

    returns: DataFrame of daily prices
    """
    grouped = transactions[["date", "ppg"]].groupby("date")
    daily = grouped.aggregate(func)

    daily["date"] = daily.index
    start = daily.date[0]
    one_year = np.timedelta64(1, "Y")
    daily["years"] = (daily.date - start) / one_year

    return daily

"""
Explanation: The following function takes a DataFrame of transactions and compute daily averages.
End of explanation
"""


def GroupByQualityAndDay(transactions):
    """Divides transactions by quality and computes mean daily price.

    transaction: DataFrame of transactions

    returns: map from quality to time series of ppg
    """
    groups = transactions.groupby("quality")
    dailies = {}
    for name, group in groups:
        dailies[name] = GroupByDay(group)

    return dailies

"""
Explanation: The following function returns a map from quality name to a DataFrame of daily averages.
End of explanation
"""


dailies = GroupByQualityAndDay(transactions)

"""
Explanation: dailies is the map from quality name to DataFrame.
End of explanation
"""


import matplotlib.pyplot as plt

thinkplot.PrePlot(rows=3)
for i, (name, daily) in enumerate(dailies.items()):
    thinkplot.SubPlot(i + 1)
    title = "Price per gram ($)" if i == 0 else ""
    thinkplot.Config(ylim=[0, 20], title=title)
    thinkplot.Scatter(daily.ppg, s=10, label=name)
    if i == 2:
        plt.xticks(rotation=30)
        thinkplot.Config()
    else:
        thinkplot.Config(xticks=[])

"""
Explanation: The following plots the daily average price for each quality.
End of explanation
"""


import statsmodels.formula.api as smf


def RunLinearModel(daily):
    model = smf.ols("ppg ~ years", data=daily)
    results = model.fit()
    return model, results

"""
Explanation: We can use statsmodels to run a linear model of price as a function of time.
End of explanation
"""


from IPython.display import display

for name, daily in dailies.items():
    model, results = RunLinearModel(daily)
    print(name)
    display(results.summary())

"""
Explanation: Here's what the results look like.
End of explanation
"""


def PlotFittedValues(model, results, label=""):
    """Plots original data and fitted values.

    model: StatsModel model object
    results: StatsModel results object
    """
    years = model.exog[:, 1]
    values = model.endog
    thinkplot.Scatter(years, values, s=15, label=label)
    thinkplot.Plot(years, results.fittedvalues, label="model", color="#ff7f00")

"""
Explanation: Now let's plot the fitted model with the data.
End of explanation
"""


def PlotLinearModel(daily, name):
    """Plots a linear fit to a sequence of prices, and the residuals.

    daily: DataFrame of daily prices
    name: string
    """
    model, results = RunLinearModel(daily)
    PlotFittedValues(model, results, label=name)
    thinkplot.Config(
        title="Fitted values",
        xlabel="Years",
        xlim=[-0.1, 3.8],
        ylabel="Price per gram ($)",
    )

"""
Explanation: The following function plots the original data and the fitted curve.
End of explanation
"""


name = "high"
daily = dailies[name]

PlotLinearModel(daily, name)

"""
Explanation: Here are results for the high quality category:
End of explanation
"""


array = np.arange(10)

"""
Explanation: Moving averages
As a simple example, I'll show the rolling average of the numbers from 1 to 10.
End of explanation
"""


series = pd.Series(array)
series.rolling(3).mean()

"""
Explanation: With a "window" of size 3, we get the average of the previous 3 elements, or nan when there are fewer than 3.
End of explanation
"""


def PlotRollingMean(daily, name):
    """Plots rolling mean.

    daily: DataFrame of daily prices
    """
    dates = pd.date_range(daily.index.min(), daily.index.max())
    reindexed = daily.reindex(dates)

    thinkplot.Scatter(reindexed.ppg, s=15, alpha=0.2, label=name)
    roll_mean = pd.Series(reindexed.ppg).rolling(30).mean()
    thinkplot.Plot(roll_mean, label="rolling mean", color="#ff7f00")
    plt.xticks(rotation=30)
    thinkplot.Config(ylabel="price per gram ($)")

"""
Explanation: The following function plots the rolling mean.
End of explanation
"""


PlotRollingMean(daily, name)

"""
Explanation: Here's what it looks like for the high quality category.
End of explanation
"""


def PlotEWMA(daily, name):
    """Plots rolling mean.

    daily: DataFrame of daily prices
    """
    dates = pd.date_range(daily.index.min(), daily.index.max())
    reindexed = daily.reindex(dates)

    thinkplot.Scatter(reindexed.ppg, s=15, alpha=0.2, label=name)
    roll_mean = reindexed.ppg.ewm(30).mean()
    thinkplot.Plot(roll_mean, label="EWMA", color="#ff7f00")
    plt.xticks(rotation=30)
    thinkplot.Config(ylabel="price per gram ($)")

PlotEWMA(daily, name)

"""
Explanation: The exponentially-weighted moving average gives more weight to more recent points.
End of explanation
"""


def FillMissing(daily, span=30):
    """Fills missing values with an exponentially weighted moving average.

    Resulting DataFrame has new columns 'ewma' and 'resid'.

    daily: DataFrame of daily prices
    span: window size (sort of) passed to ewma

    returns: new DataFrame of daily prices
    """
    dates = pd.date_range(daily.index.min(), daily.index.max())
    reindexed = daily.reindex(dates)

    ewma = pd.Series(reindexed.ppg).ewm(span=span).mean()

    resid = (reindexed.ppg - ewma).dropna()
    fake_data = ewma + thinkstats2.Resample(resid, len(reindexed))
    reindexed.ppg.fillna(fake_data, inplace=True)

    reindexed["ewma"] = ewma
    reindexed["resid"] = reindexed.ppg - ewma
    return reindexed

def PlotFilled(daily, name):
    """Plots the EWMA and filled data.

    daily: DataFrame of daily prices
    """
    filled = FillMissing(daily, span=30)
    thinkplot.Scatter(filled.ppg, s=15, alpha=0.2, label=name)
    thinkplot.Plot(filled.ewma, label="EWMA", color="#ff7f00")
    plt.xticks(rotation=30)
    thinkplot.Config(ylabel="Price per gram ($)")

"""
Explanation: We can use resampling to generate missing values with the right amount of noise.
End of explanation
"""


PlotFilled(daily, name)

"""
Explanation: Here's what the EWMA model looks like with missing values filled.
End of explanation
"""


def SerialCorr(series, lag=1):
    xs = series[lag:]
    ys = series.shift(lag)[lag:]
    corr = thinkstats2.Corr(xs, ys)
    return corr

"""
Explanation: Serial correlation
The following function computes serial correlation with the given lag.
End of explanation
"""


filled_dailies = {}
for name, daily in dailies.items():
    filled_dailies[name] = FillMissing(daily, span=30)

"""
Explanation: Before computing correlations, we'll fill missing values.
End of explanation
"""


for name, filled in filled_dailies.items():
    corr = thinkstats2.SerialCorr(filled.ppg, lag=1)
    print(name, corr)

"""
Explanation: Here are the serial correlations for raw price data.
End of explanation
"""


for name, filled in filled_dailies.items():
    corr = thinkstats2.SerialCorr(filled.resid, lag=1)
    print(name, corr)

"""
Explanation: It's not surprising that there are correlations between consecutive days, because there are obvious trends in the data.
It is more interested to see whether there are still correlations after we subtract away the trends.
End of explanation
"""


rows = []
for lag in [1, 7, 30, 365]:
    print(lag, end="\t")
    for name, filled in filled_dailies.items():
        corr = SerialCorr(filled.resid, lag)
        print("%.2g" % corr, end="\t")
    print()

"""
Explanation: Even if the correlations between consecutive days are weak, there might be correlations across intervals of one week, one month, or one year.
End of explanation
"""


# NOTE: acf throws a FutureWarning because we need to replace `unbiased` with `adjusted`,
# just as soon as Colab gets updated :)

import warnings

warnings.simplefilter(action="ignore", category=FutureWarning)

import statsmodels.tsa.stattools as smtsa

filled = filled_dailies["high"]
acf = smtsa.acf(filled.resid, nlags=365, unbiased=True, fft=False)
print("%0.2g, %.2g, %0.2g, %0.2g, %0.2g" % (acf[0], acf[1], acf[7], acf[30], acf[365]))

"""
Explanation: The strongest correlation is a weekly cycle in the medium quality category.
Autocorrelation
The autocorrelation function is the serial correlation computed for all lags.
We can use it to replicate the results from the previous section.
End of explanation
"""


def SimulateAutocorrelation(daily, iters=1001, nlags=40):
    """Resample residuals, compute autocorrelation, and plot percentiles.

    daily: DataFrame
    iters: number of simulations to run
    nlags: maximum lags to compute autocorrelation
    """
    # run simulations
    t = []
    for _ in range(iters):
        filled = FillMissing(daily, span=30)
        resid = thinkstats2.Resample(filled.resid)
        acf = smtsa.acf(resid, nlags=nlags, unbiased=True, fft=False)[1:]
        t.append(np.abs(acf))

    high = thinkstats2.PercentileRows(t, [97.5])[0]
    low = -high
    lags = range(1, nlags + 1)
    thinkplot.FillBetween(lags, low, high, alpha=0.2, color="gray")

"""
Explanation: To get a sense of how much autocorrelation we should expect by chance, we can resample the data (which eliminates any actual autocorrelation) and compute the ACF.
End of explanation
"""


def PlotAutoCorrelation(dailies, nlags=40, add_weekly=False):
    """Plots autocorrelation functions.

    dailies: map from category name to DataFrame of daily prices
    nlags: number of lags to compute
    add_weekly: boolean, whether to add a simulated weekly pattern
    """
    thinkplot.PrePlot(3)
    daily = dailies["high"]
    SimulateAutocorrelation(daily)

    for name, daily in dailies.items():

        if add_weekly:
            daily.ppg = AddWeeklySeasonality(daily)

        filled = FillMissing(daily, span=30)

        acf = smtsa.acf(filled.resid, nlags=nlags, unbiased=True, fft=False)
        lags = np.arange(len(acf))
        thinkplot.Plot(lags[1:], acf[1:], label=name)

"""
Explanation: The following function plots the actual autocorrelation for lags up to 40 days.
The flag add_weekly indicates whether we should add a simulated weekly cycle.
End of explanation
"""


def AddWeeklySeasonality(daily):
    """Adds a weekly pattern.

    daily: DataFrame of daily prices

    returns: new DataFrame of daily prices
    """
    fri_or_sat = (daily.index.dayofweek == 4) | (daily.index.dayofweek == 5)
    fake = daily.ppg.copy()
    fake[fri_or_sat] += np.random.uniform(0, 2, fri_or_sat.sum())
    return fake

"""
Explanation: To show what a strong weekly cycle would look like, we have the option of adding a price increase of 1-2 dollars on Friday and Saturdays.
End of explanation
"""


axis = [0, 41, -0.2, 0.2]

PlotAutoCorrelation(dailies, add_weekly=False)
thinkplot.Config(axis=axis, loc="lower right", ylabel="correlation", xlabel="lag (day)")

"""
Explanation: Here's what the real ACFs look like.  The gray regions indicate the levels we expect by chance.
End of explanation
"""


PlotAutoCorrelation(dailies, add_weekly=True)
thinkplot.Config(axis=axis, loc="lower right", xlabel="lag (days)")

"""
Explanation: Here's what it would look like if there were a weekly cycle.
End of explanation
"""


def GenerateSimplePrediction(results, years):
    """Generates a simple prediction.

    results: results object
    years: sequence of times (in years) to make predictions for

    returns: sequence of predicted values
    """
    n = len(years)
    inter = np.ones(n)
    d = dict(Intercept=inter, years=years, years2=years**2)
    predict_df = pd.DataFrame(d)
    predict = results.predict(predict_df)
    return predict

def PlotSimplePrediction(results, years):
    predict = GenerateSimplePrediction(results, years)

    thinkplot.Scatter(daily.years, daily.ppg, alpha=0.2, label=name)
    thinkplot.plot(years, predict, color="#ff7f00")
    xlim = years[0] - 0.1, years[-1] + 0.1
    thinkplot.Config(
        title="Predictions",
        xlabel="Years",
        xlim=xlim,
        ylabel="Price per gram ($)",
        loc="upper right",
    )

"""
Explanation: Prediction
The simplest way to generate predictions is to use statsmodels to fit a model to the data, then use the predict method from the results.
End of explanation
"""


name = "high"
daily = dailies[name]

_, results = RunLinearModel(daily)
years = np.linspace(0, 5, 101)
PlotSimplePrediction(results, years)

"""
Explanation: Here's what the prediction looks like for the high quality category, using the linear model.
End of explanation
"""


def SimulateResults(daily, iters=101, func=RunLinearModel):
    """Run simulations based on resampling residuals.

    daily: DataFrame of daily prices
    iters: number of simulations
    func: function that fits a model to the data

    returns: list of result objects
    """
    _, results = func(daily)
    fake = daily.copy()

    result_seq = []
    for _ in range(iters):
        fake.ppg = results.fittedvalues + thinkstats2.Resample(results.resid)
        _, fake_results = func(fake)
        result_seq.append(fake_results)

    return result_seq

"""
Explanation: When we generate predictions, we want to quatify the uncertainty in the prediction.  We can do that by resampling.  The following function fits a model to the data, computes residuals, then resamples from the residuals to general fake datasets.  It fits the same model to each fake dataset and returns a list of results.
End of explanation
"""


def GeneratePredictions(result_seq, years, add_resid=False):
    """Generates an array of predicted values from a list of model results.

    When add_resid is False, predictions represent sampling error only.

    When add_resid is True, they also include residual error (which is
    more relevant to prediction).

    result_seq: list of model results
    years: sequence of times (in years) to make predictions for
    add_resid: boolean, whether to add in resampled residuals

    returns: sequence of predictions
    """
    n = len(years)
    d = dict(Intercept=np.ones(n), years=years, years2=years**2)
    predict_df = pd.DataFrame(d)

    predict_seq = []
    for fake_results in result_seq:
        predict = fake_results.predict(predict_df)
        if add_resid:
            predict += thinkstats2.Resample(fake_results.resid, n)
        predict_seq.append(predict)

    return predict_seq

"""
Explanation: To generate predictions, we take the list of results fitted to resampled data.  For each model, we use the predict method to generate predictions, and return a sequence of predictions.
If add_resid is true, we add resampled residuals to the predicted values, which generates predictions that include predictive uncertainty (due to random noise) as well as modeling uncertainty (due to random sampling).
End of explanation
"""


def PlotPredictions(daily, years, iters=101, percent=90, func=RunLinearModel):
    """Plots predictions.

    daily: DataFrame of daily prices
    years: sequence of times (in years) to make predictions for
    iters: number of simulations
    percent: what percentile range to show
    func: function that fits a model to the data
    """
    result_seq = SimulateResults(daily, iters=iters, func=func)
    p = (100 - percent) / 2
    percents = p, 100 - p

    predict_seq = GeneratePredictions(result_seq, years, add_resid=True)
    low, high = thinkstats2.PercentileRows(predict_seq, percents)
    thinkplot.FillBetween(years, low, high, alpha=0.3, color="gray")

    predict_seq = GeneratePredictions(result_seq, years, add_resid=False)
    low, high = thinkstats2.PercentileRows(predict_seq, percents)
    thinkplot.FillBetween(years, low, high, alpha=0.5, color="gray")

"""
Explanation: To visualize predictions, I show a darker region that quantifies modeling uncertainty and a lighter region that quantifies predictive uncertainty.
End of explanation
"""


years = np.linspace(0, 5, 101)
thinkplot.Scatter(daily.years, daily.ppg, alpha=0.1, label=name)
PlotPredictions(daily, years)
xlim = years[0] - 0.1, years[-1] + 0.1
thinkplot.Config(
    title="Predictions", xlabel="Years", xlim=xlim, ylabel="Price per gram ($)"
)

"""
Explanation: Here are the results for the high quality category.
End of explanation
"""


def SimulateIntervals(daily, iters=101, func=RunLinearModel):
    """Run simulations based on different subsets of the data.

    daily: DataFrame of daily prices
    iters: number of simulations
    func: function that fits a model to the data

    returns: list of result objects
    """
    result_seq = []
    starts = np.linspace(0, len(daily), iters).astype(int)

    for start in starts[:-2]:
        subset = daily[start:]
        _, results = func(subset)
        fake = subset.copy()

        for _ in range(iters):
            fake.ppg = results.fittedvalues + thinkstats2.Resample(results.resid)
            _, fake_results = func(fake)
            result_seq.append(fake_results)

    return result_seq

"""
Explanation: But there is one more source of uncertainty: how much past data should we use to build the model?
The following function generates a sequence of models based on different amounts of past data.
End of explanation
"""


def PlotIntervals(daily, years, iters=101, percent=90, func=RunLinearModel):
    """Plots predictions based on different intervals.

    daily: DataFrame of daily prices
    years: sequence of times (in years) to make predictions for
    iters: number of simulations
    percent: what percentile range to show
    func: function that fits a model to the data
    """
    result_seq = SimulateIntervals(daily, iters=iters, func=func)
    p = (100 - percent) / 2
    percents = p, 100 - p

    predict_seq = GeneratePredictions(result_seq, years, add_resid=True)
    low, high = thinkstats2.PercentileRows(predict_seq, percents)
    thinkplot.FillBetween(years, low, high, alpha=0.2, color="gray")

"""
Explanation: And this function plots the results.
End of explanation
"""


name = "high"
daily = dailies[name]

thinkplot.Scatter(daily.years, daily.ppg, alpha=0.1, label=name)
PlotIntervals(daily, years)
PlotPredictions(daily, years)
xlim = years[0] - 0.1, years[-1] + 0.1
thinkplot.Config(
    title="Predictions", xlabel="Years", xlim=xlim, ylabel="Price per gram ($)"
)

"""
Explanation: Here's what the high quality category looks like if we take into account uncertainty about how much past data to use.
End of explanation
"""


# Solution


def RunQuadraticModel(daily):
    """Runs a linear model of prices versus years.

    daily: DataFrame of daily prices

    returns: model, results
    """
    daily["years2"] = daily.years**2
    model = smf.ols("ppg ~ years + years2", data=daily)
    results = model.fit()
    return model, results

# Solution

name = "high"
daily = dailies[name]

model, results = RunQuadraticModel(daily)
results.summary()

# Solution

PlotFittedValues(model, results, label=name)
thinkplot.Config(
    title="Fitted values", xlabel="Years", xlim=[-0.1, 3.8], ylabel="price per gram ($)"
)

# Solution

years = np.linspace(0, 5, 101)
thinkplot.Scatter(daily.years, daily.ppg, alpha=0.1, label=name)
PlotPredictions(daily, years, func=RunQuadraticModel)
thinkplot.Config(
    title="predictions",
    xlabel="Years",
    xlim=[years[0] - 0.1, years[-1] + 0.1],
    ylabel="Price per gram ($)",
)

"""
Explanation: Exercises
Exercise:   The linear model I used in this chapter has the obvious drawback that it is linear, and there is no reason to expect prices to change linearly over time. We can add flexibility to the model by adding a quadratic term, as we did in Section 11.3.
Use a quadratic model to fit the time series of daily prices, and use the model to generate predictions. You will have to write a version of RunLinearModel that runs that quadratic model, but after that you should be able to reuse code from the chapter to generate predictions.
End of explanation
"""


# Solution


class SerialCorrelationTest(thinkstats2.HypothesisTest):
    """Tests serial correlations by permutation."""

    def TestStatistic(self, data):
        """Computes the test statistic.

        data: tuple of xs and ys
        """
        series, lag = data
        test_stat = abs(SerialCorr(series, lag))
        return test_stat

    def RunModel(self):
        """Run the model of the null hypothesis.

        returns: simulated data
        """
        series, lag = self.data
        permutation = series.reindex(np.random.permutation(series.index))
        return permutation, lag

# Solution

# test the correlation between consecutive prices

name = "high"
daily = dailies[name]

series = daily.ppg
test = SerialCorrelationTest((series, 1))
pvalue = test.PValue()
print(test.actual, pvalue)

# Solution

# test for serial correlation in residuals of the linear model

_, results = RunLinearModel(daily)
series = results.resid
test = SerialCorrelationTest((series, 1))
pvalue = test.PValue()
print(test.actual, pvalue)

# Solution

# test for serial correlation in residuals of the quadratic model

_, results = RunQuadraticModel(daily)
series = results.resid
test = SerialCorrelationTest((series, 1))
pvalue = test.PValue()
print(test.actual, pvalue)

"""
Explanation: Exercise: Write a definition for a class named SerialCorrelationTest that extends HypothesisTest from Section 9.2. It should take a series and a lag as data, compute the serial correlation of the series with the given lag, and then compute the p-value of the observed correlation.
Use this class to test whether the serial correlation in raw price data is statistically significant. Also test the residuals of the linear model and (if you did the previous exercise), the quadratic model.
End of explanation
"""


name = "high"
daily = dailies[name]

filled = FillMissing(daily)
diffs = filled.ppg.diff()

thinkplot.plot(diffs)
plt.xticks(rotation=30)
thinkplot.Config(ylabel="Daily change in price per gram ($)")

filled["slope"] = diffs.ewm(span=365).mean()
thinkplot.plot(filled.slope[-365:])
plt.xticks(rotation=30)
thinkplot.Config(ylabel="EWMA of diff ($)")

# extract the last inter and the mean of the last 30 slopes
start = filled.index[-1]
inter = filled.ewma[-1]
slope = filled.slope[-30:].mean()

start, inter, slope

# reindex the DataFrame, adding a year to the end
dates = pd.date_range(filled.index.min(), filled.index.max() + np.timedelta64(365, "D"))
predicted = filled.reindex(dates)

# generate predicted values and add them to the end
predicted["date"] = predicted.index
one_day = np.timedelta64(1, "D")
predicted["days"] = (predicted.date - start) / one_day
predict = inter + slope * predicted.days
predicted.ewma.fillna(predict, inplace=True)

# plot the actual values and predictions
thinkplot.Scatter(daily.ppg, alpha=0.1, label=name)
thinkplot.Plot(predicted.ewma, color="#ff7f00")

"""
Explanation: Bonus Example: There are several ways to extend the EWMA model to generate predictions. One of the simplest is something like this:


Compute the EWMA of the time series and use the last point as an intercept, inter.


Compute the EWMA of differences between successive elements in the time series and use the last point as a slope, slope.


To predict values at future times, compute inter + slope * dt, where dt is the difference between the time of the prediction and the time of the last observation.
End of explanation
"""


