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The subject of this report is whether the fluctuation of cryptocurrency can explain the change in the stock price of Tesla. Since Tesla announced that they accept cryptocurrency to buy their products Tesla and holds about 2 billion dollars, some financial analysts have claimed that the effect of the volatility of cryptocurrency is huge for the stock price of Tesla. Furthermore, As the stock price of Tesla has skyrocketed since the pandemic, Elon Musk, CEO of Tesla, has influenced not only the stock price but also the price of cryptocurrency especially the DOGE coin. We will use two methods for forecasting 1) the traditional approach: forecasting the stock price through VAR(Vector auto-regression with whole variables). 2) LASSO approach: forecasting it through VAR with LASSO eliminating the variables that have low coefficients.

Research purpose

Whether it is possible that the fluctuation of cryptocurrency explains the change of the stock price of Tesla and which approach can forecast the stock price better.

Methods of analysis

  1. Setting up variables The following 10 cryptocurrencies are exogenous variables based on the market value.
  • Bitcoin, Ethereum, Binance, Cardano, Tether, Ripple, Solana, Kraken, USD Coin, and Dogecoin

In addition, we also control for the following variables:

i) Treasury bond yield: as an opportunity cost of the stock price, it has a negative effect on the stock price

ii) Fed Funds Rate: Higher rates indicate that the economy is heating up (more consumption) and vice-versa.

iii) Inflation (inflation expectation and 10-year break-even inflation): relating the purchasing power of customers and stimulating the increase of interest rates

iv) Trade Weighted Dollar Index: TWD can influence the export and import of products along with the fluctuation of stock price

v) Oil price: A higher oil price may cause people to switch to buy an electric car in which case, the price of Tesla’s company would rise. vi) Gold and Silver prices: As a safety asset, the prices of both silver and gold can have a negative relationship with the stock price

the independent variable is the stock price of Tesla

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import statsmodels.api as sm
from statsmodels.tsa.ar_model import AutoReg
import numpy as np
from sklearn.linear_model import ElasticNetCV, ElasticNet
from sklearn.metrics import mean_squared_error
from sklearn.linear_model import LassoCV
import warnings
warnings.simplefilter('ignore')
from sklearn import (linear_model, metrics, neural_network, pipeline, preprocessing, model_selection)
import seaborn as sns
sns.set()
import datetime as dt
from statsmodels.tsa.stattools import grangercausalitytests

dset = pd.read_csv('TSLA_ds_1022.csv')
dset = dset.drop(0)
dset = dset.set_index("Date")
dset.head()
TSLA 10CMR FFR infexp TWD 10YBE oil XAU XAG BTC ... ETH_diff BNB_diff ADA_diff Tether_diff XRP_diff SOL_diff pDOTn_diff USDC_diff DOGE_diff const
Date
2016-01-05 44.69 2.25 0.36 1.81 114.2649 1.56 35.97 1077.66 13.98 431.8 ... 0.0 0.0 0.0 0.0 2.0000 0.0 0.0 0.0 0.0 1
2016-01-06 43.81 2.18 0.36 1.80 114.6177 1.53 33.97 1094.45 14.01 428.0 ... 0.0 0.0 0.0 0.0 0.0000 0.0 0.0 0.0 0.0 1
2016-01-07 43.13 2.16 0.36 1.75 114.6517 1.50 33.29 1109.25 14.31 459.0 ... 0.0 0.0 0.0 0.0 0.0000 0.0 0.0 0.0 0.0 1
2016-01-08 42.20 2.13 0.36 1.73 115.0097 1.48 33.20 1104.24 13.95 454.0 ... 0.0 0.0 0.0 0.0 0.0000 0.0 0.0 0.0 0.0 1
2016-01-11 41.57 2.17 0.36 1.71 115.0141 1.45 31.42 1094.26 13.86 449.3 ... 0.0 0.0 0.0 0.0 24.6883 0.0 0.0 0.0 0.0 1

5 rows × 39 columns

Analyzing the Granger Causality

In the result of Granger Causality analysis, all cryptocurrency variables have a probability greater than 5%. Therefore, the variables of cryptocurrency do not have a significant effect on the traditional approach.

maxlag=10
test = 'ssr_chi2test'
def grangers_causation_matrix(data, variables, test='ssr_chi2test', verbose=False):    
    """Check Granger Causality of all possible combinations of the Time series.
    The rows are the response variable, columns are predictors. The values in the table 
    are the P-Values. P-Values lesser than the significance level (0.05), implies 
    the Null Hypothesis that the coefficients of the corresponding past values is 
    zero, that is, the X does not cause Y can be rejected.

    data      : pandas dataframe containing the time series variables
    variables : list containing names of the time series variables.
    """
    df = pd.DataFrame(np.zeros((len(variables), len(variables))), columns=variables, index=variables)
    for c in df.columns:
        for r in df.index:
            test_result = grangercausalitytests(data[[r, c]], maxlag=maxlag, verbose=False)
            p_values = [round(test_result[i+1][0][test][1],4) for i in range(maxlag)]
            if verbose: print(f'Y = {r}, X = {c}, P Values = {p_values}')
            min_p_value = np.min(p_values)
            df.loc[r, c] = min_p_value
    df.columns = [var + '_x' for var in variables]
    df.index = [var + '_y' for var in variables]
    return df

Granger = dset.loc[:, "TSLA_diff":"DOGE_diff"]
grangers_causation_matrix(Granger, variables = Granger.columns)
TSLA_diff_x 10CMR_diff_x FFR_diff_x infexp_diff_x TWD_diff_x 10YBE_diff_x oil_diff_x XAU_diff_x XAG_diff_x BTC_diff_x ETH_diff_x BNB_diff_x ADA_diff_x Tether_diff_x XRP_diff_x SOL_diff_x pDOTn_diff_x USDC_diff_x DOGE_diff_x
TSLA_diff_y 1.0000 0.6571 0.1963 0.4127 0.2082 0.1380 0.8005 0.0007 0.0096 0.6192 0.4485 0.9632 0.5514 0.9211 0.3492 0.8981 0.7859 0.8515 0.8469
10CMR_diff_y 0.0091 1.0000 0.0000 0.0000 0.0010 0.0000 0.0063 0.0000 0.0001 0.0000 0.0002 0.2052 0.0001 0.6290 0.0214 0.1545 0.0431 0.7412 0.4359
FFR_diff_y 0.0879 0.0000 1.0000 0.0000 0.0000 0.0000 0.0005 0.0000 0.0000 0.0000 0.0000 0.4487 0.0000 0.9813 0.0001 0.5253 0.8308 0.8973 0.8941
infexp_diff_y 0.4964 0.0000 0.0000 1.0000 0.0002 0.0000 0.0000 0.0067 0.0000 0.0000 0.0000 0.3346 0.0000 0.0065 0.1274 0.3326 0.5260 0.4813 0.6607
TWD_diff_y 0.4741 0.0009 0.0000 0.0000 1.0000 0.0000 0.2020 0.0000 0.0000 0.0007 0.0000 0.6265 0.0104 0.3737 0.3939 0.6338 0.3210 0.2664 0.8202
10YBE_diff_y 0.7924 0.0000 0.0000 0.0000 0.0154 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7873 0.0000 0.8048 0.0012 0.4042 0.3702 0.5009 0.8122
oil_diff_y 0.6599 0.0000 0.0107 0.0000 0.0259 0.0000 1.0000 0.0001 0.2883 0.4544 0.3266 0.6329 0.7146 0.9673 0.5308 0.9539 0.7794 0.8809 0.9600
XAU_diff_y 0.0261 0.0000 0.0000 0.0390 0.5379 0.0000 0.0409 1.0000 0.0050 0.0009 0.0118 0.1037 0.3502 0.5957 0.5645 0.4666 0.7449 0.4006 0.8543
XAG_diff_y 0.3175 0.0000 0.0082 0.0337 0.1683 0.0000 0.5411 0.0126 1.0000 0.0051 0.0107 0.5948 0.0260 0.4045 0.4021 0.0001 0.3679 0.6546 0.4319
BTC_diff_y 0.7210 0.0136 0.0491 0.3187 0.0040 0.0734 0.4174 0.0213 0.1035 1.0000 0.0116 0.2759 0.0452 0.6021 0.0607 0.1768 0.5764 0.4664 0.7431
ETH_diff_y 0.0000 0.0363 0.0885 0.1287 0.0091 0.0976 0.3597 0.4238 0.6921 0.0062 1.0000 0.3661 0.1468 0.3435 0.0898 0.7666 0.4659 0.7766 0.6625
BNB_diff_y 0.8345 0.7036 0.3885 0.4279 0.7411 0.6453 0.9371 0.6083 0.8366 0.3796 0.5876 1.0000 0.1206 0.6467 0.0745 0.0412 0.4296 0.3453 0.6194
ADA_diff_y 0.7034 0.0912 0.3040 0.0432 0.5556 0.0284 0.3320 0.0443 0.4985 0.0004 0.0477 0.0245 1.0000 0.5514 0.0004 0.0650 0.1236 0.4002 0.2660
Tether_diff_y 0.9104 0.8093 0.9815 0.7463 0.0559 0.6725 0.9786 0.2917 0.5475 0.0700 0.1434 0.0008 0.0003 1.0000 0.0000 0.9261 0.9519 0.7658 0.9077
XRP_diff_y 0.6536 0.5104 0.2915 0.2571 0.3972 0.2159 0.8442 0.2406 0.6087 0.0201 0.0903 0.0270 0.0012 0.1630 1.0000 0.5952 0.2933 0.6438 0.5779
SOL_diff_y 0.7142 0.0926 0.4007 0.3217 0.7922 0.4763 0.9589 0.1414 0.0322 0.3276 0.2857 0.3227 0.0004 0.8986 0.0000 1.0000 0.0000 0.9475 0.9911
pDOTn_diff_y 0.8101 0.1768 0.4263 0.8178 0.1299 0.5545 0.9439 0.0013 0.0000 0.2988 0.1380 0.7665 0.3767 0.9649 0.0016 0.0024 1.0000 0.9831 0.9593
USDC_diff_y 0.8319 0.4363 0.9091 0.5988 0.2546 0.5857 0.9543 0.4587 0.5843 0.0244 0.2662 0.1003 0.0029 0.8840 0.6250 0.9224 0.9979 1.0000 0.9930
DOGE_diff_y 0.7456 0.6685 0.9377 0.7775 0.8012 0.6029 0.9161 0.5163 0.5112 0.3599 0.2325 0.4398 0.3318 0.9068 0.5919 0.9506 0.9652 0.9761 1.0000

Confirm training period and test period

We created three time periods of the training set. The first set starts with the beginning of 2016 when cryptocurrencies became famous. The second set starts with the beginning of 2017 when cryptocurrency skyrocketed the first time. The third set starts with the beginning of 2020 when both Tesla and cryptocurrencies skyrocketed. Because the third set only represents that LASSO does not eliminate the coefficient of cryptocurrencies and we realized that the current relationship between the stock price of Tesla and the fluctuations of cryptocurrencies is stronger than before, we decide to choose the Third set as a training set. Furthermore, we confirmed that the test period from Jul-01-2021 to Oct-18-2021.

TSLA = dset["TSLA_diff"]
Exogen = dset.loc[:, "10CMR_diff":"DOGE_diff"]
TSLA_OLS = sm.OLS(TSLA, Exogen)
result_OLS = TSLA_OLS.fit()

names = dset.columns.values[1:19]
plt.figure(figsize=(15,5))
plt.bar(names,result_OLS.params[0:])
plt.title('Relationship 2016-01-01 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('OLS Estimates');
print(result_OLS.params[0:])

10CMR_diff     0.014131
FFR_diff       0.092686
infexp_diff    0.087457
TWD_diff      -1.309505
10YBE_diff     0.015982
oil_diff      -0.011928
XAU_diff      -1.087257
XAG_diff       0.463873
BTC_diff       0.020326
ETH_diff       0.017720
BNB_diff      -0.004339
ADA_diff       0.013301
Tether_diff   -0.002773
XRP_diff      -0.020046
SOL_diff       0.026030
pDOTn_diff     0.036460
USDC_diff      0.026032
DOGE_diff      0.000118
dtype: float64

family_1

TSLA_EN = LassoCV(cv=10, random_state=1)
TSLA_EN.fit(Exogen, TSLA)

plt.figure(figsize=(15,5))
plt.bar(names, TSLA_EN.coef_)
plt.title('Relationship 2016-01-01 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('Lasso Estimates');
print(TSLA_EN.coef_)

[ 0.          0.05427374  0.         -0.          0.         -0.
 -0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.        ]

family_1

TSLA = dset.loc["2017-01-01": ,"TSLA_diff"]
Exogen = dset.loc["2017-01-01": , "10CMR_diff":"DOGE_diff"]
TSLA_OLS = sm.OLS(TSLA, Exogen)
result_OLS = TSLA_OLS.fit()

names = dset.columns.values[1:19]
plt.figure(figsize=(15,5))
plt.bar(names,result_OLS.params[0:])
plt.title('Relationship 2017-01-01 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('OLS Estimates');
print(result_OLS.params[0:])

10CMR_diff     0.080909
FFR_diff       0.018976
infexp_diff   -0.210880
TWD_diff      -1.256933
10YBE_diff     0.298315
oil_diff      -0.006214
XAU_diff      -0.544770
XAG_diff       0.468780
BTC_diff       0.009931
ETH_diff       0.021716
BNB_diff      -0.005463
ADA_diff      -0.009273
Tether_diff    0.006178
XRP_diff       0.017648
SOL_diff       0.021012
pDOTn_diff     0.026336
USDC_diff      0.027537
DOGE_diff      0.000150
dtype: float64

family_1

TSLA_EN = LassoCV(cv=10, random_state=1)
TSLA_EN.fit(Exogen, TSLA)

plt.figure(figsize=(15,5))
plt.bar(names, TSLA_EN.coef_)
plt.title('Relationship 2017-01-01 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('Lasso Estimates');
print(TSLA_EN.coef_)

[ 0.04315125  0.03434962  0.         -0.          0.06338159 -0.00461966
  0.          0.05125903  0.          0.02463747 -0.          0.
  0.          0.0127104   0.02291635  0.00664378  0.          0.00013601]

family_1

TSLA = dset.loc["2020-01-02": ,"TSLA_diff"]
Exogen = dset.loc["2020-01-02": , "10CMR_diff":"DOGE_diff"]
TSLA_OLS = sm.OLS(TSLA, Exogen)
result_OLS = TSLA_OLS.fit()

names = dset.columns.values[1:19]
plt.figure(figsize=(15,5))
plt.bar(names,result_OLS.params[0:])
plt.title('Relationship 2020-01-02 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('OLS Estimates');
print(result_OLS.params[0:])

10CMR_diff     0.068849
FFR_diff       0.017995
infexp_diff   -0.398306
TWD_diff      -2.191456
10YBE_diff     0.380097
oil_diff      -0.006267
XAU_diff      -0.312150
XAG_diff       0.398949
BTC_diff       0.071159
ETH_diff       0.036119
BNB_diff      -0.023011
ADA_diff      -0.021280
Tether_diff    3.290954
XRP_diff       0.046905
SOL_diff       0.012452
pDOTn_diff     0.000428
USDC_diff      2.495569
DOGE_diff      0.000170
dtype: float64

family_1

TSLA_EN = LassoCV(cv=10, random_state=1)
TSLA_EN.fit(Exogen, TSLA)

plt.figure(figsize=(15,5))
plt.bar(names, TSLA_EN.coef_)
plt.title('Relationship 2020-01-02 ~ 2021-10-19')
plt.xlabel('Intercept and Coefficients')
plt.ylabel('Lasso Estimates');
print(TSLA_EN.coef_)

[ 0.00260532  0.04136176  0.         -0.          0.00862294 -0.00686096
  0.          0.          0.00785282  0.07127208 -0.          0.
  0.          0.03075644  0.01217944  0.         -0.          0.00015222]

family_1

"""alphas = [0.0001, 0.001, 0.01, 0.1, 0.3, 0.5, 0.7, 1]
for a in alphas:
    model = ElasticNet(alpha=a).fit(Exogen,TSLA)   
    score = model.score(Exogen,TSLA)
    pred_y = model.predict(Exogen)
    mse = mean_squared_error(TSLA, pred_y)
    print("Alpha:{0:.4f}, R2:{1:.2f}, MSE:{2:.2f}, RMSE:{3:.2f}"
       .format(a, score, mse, np.sqrt(mse))) """

'alphas = [0.0001, 0.001, 0.01, 0.1, 0.3, 0.5, 0.7, 1]\nfor a in alphas:\n    model = ElasticNet(alpha=a).fit(Exogen,TSLA)   \n    score = model.score(Exogen,TSLA)\n    pred_y = model.predict(Exogen)\n    mse = mean_squared_error(TSLA, pred_y)\n    print("Alpha:{0:.4f}, R2:{1:.2f}, MSE:{2:.2f}, RMSE:{3:.2f}"\n       .format(a, score, mse, np.sqrt(mse))) '

from statsmodels.tsa.vector_ar.var_model import VAR

dset1 = pd.read_csv('TSLA_ds_1022.csv')
dset1 = dset1.drop(0)
dset1 = dset1.set_index("Date")
names1 = ["TSLA_diff", "10CMR_diff", "FFR_diff", "infexp_diff", "TWD_diff", "10YBE_diff",\
          "oil_diff", "XAU_diff", "XAG_diff", "BTC_diff", "ETH_diff", "BNB_diff",\
          "ADA_diff", "Tether_diff", "XRP_diff", "SOL_diff", "pDOTn_diff", "USDC_diff", "DOGE_diff"]
names2 = ["10CMR_diff", "FFR_diff", "infexp_diff", "TWD_diff", "10YBE_diff",\
          "oil_diff", "XAU_diff", "XAG_diff", "BTC_diff", "ETH_diff", "BNB_diff",\
          "ADA_diff", "Tether_diff", "XRP_diff", "SOL_diff", "pDOTn_diff", "USDC_diff", "DOGE_diff"]

dset2 = dset1.loc[:,names1]
#data_t = dset2.loc["2016-01-04":"2021-06-21", :]

#col_mask=dset2.isnull().any(axis=0) 
#row_mask=dset2.isnull().any(axis=1)
#print(dset2.loc[row_mask,col_mask])

#dset2.fillna(dset2.mean(), inplace=True)
#dset2 = dset2.fillna(dset2.mean())
#dset2._is_view

start_date = "2021-06-21"
end_date = "2021-10-19"

dset2.index.names = ["Date"]
dset2.index = pd.to_datetime(dset.index)
dset2.to_period("D")

data_train = dset2.loc["2016-01-05":"2021-06-21", :]
var_train = VAR(data_train)
results = var_train.fit(25)
lag_order = results.k_ar
forecasted = pd.DataFrame(results.forecast(data_train.values[-lag_order:], 120)) # Forecast 120 months


# Rename forecasted columns
forecasted_names = list(forecasted.columns.values)
data_train_names = list(data_train.columns.values)

var_dict = dict(zip(forecasted_names, data_train_names))
for f,t in var_dict.items():
    forecasted = forecasted.rename(columns={f:t + "_fcast"})
    
forecasted.index= pd.DatetimeIndex(pd.date_range(start_date, periods=forecasted.shape[0]))
forecasted.index.names = ["Date"]

# Parse together forecasted data with original dataset
final_data = pd.merge(forecasted, dset2, left_index=True, right_index=True)
final_data = final_data.sort_index(axis=0, ascending=True)
final_data = pd.concat([data_train, final_data], sort=True, axis=0)
final_data = final_data.sort_index(axis=0, ascending=True)

TSLA_fs = final_data.loc["2021-06-22":"2021-10-18","TSLA_diff_fcast"]
TSLA_r = final_data.loc["2021-06-22":"2021-10-18","TSLA_diff"]

print(TSLA_fs)
var_mse1 = metrics.mean_squared_error(TSLA_fs, TSLA_r)

Date
2021-06-22    0.101006
2021-06-23    5.433423
2021-06-24   -7.929520
2021-06-25    0.569414
2021-06-28    2.115058
                ...   
2021-10-12   -0.075105
2021-10-13    0.118774
2021-10-14    0.335843
2021-10-15   -0.108588
2021-10-18    0.121682
Name: TSLA_diff_fcast, Length: 83, dtype: float64

print(f"The mean squared error between the forecasted and actual values is {var_mse1}")

The mean squared error between the forecasted and actual values is 17.311018428934627

Results of forecasting

The MSE(Mean squared error) of forecasting the stock price through VAR(Vector auto -regression) with the traditional model is 17.3110. The MSE of forecasting the stock price through VAR with the LASSO model is 10.6772.

fig, ax = plt.subplots(figsize=(14,6))
colors = sns.color_palette("deep", 8)

TSLA_rplot = final_data.loc["2021-01-02":"2021-10-18","TSLA_diff"]

TSLA_fs.plot(ax=ax, legend=True, linewidth=2.5, linestyle="dashed")
TSLA_rplot.plot(ax=ax, legend=True, alpha=0.6, linestyle="solid")

ax.set_title("VAR in-sample forecast, traditional approach", fontsize=16, fontweight="bold", fontname="Verdana", loc="left")
ax.set_ylabel("First differences", fontname="Verdana")
ax.legend([f"VAR Forecast, MSE={var_mse1}", "TSLA Real Fluctuations"])

<matplotlib.legend.Legend at 0x272c5e19550>

family_1

def train_test_plot(model, X_train, X_test):
    """
    This will plot the actual values of CPI against the one fitted by the model
    We train the model until 2009 and then use it from 2009 onwards on the test features dataset
    """
    fig, ax = plt.subplots(figsize=(12,4))
    colors = sns.color_palette("deep", 8)
    
    yvalues = pd.DataFrame(y_test)
    
    forecasted = list(model.predict(X_test)) # Use the model fit on features data from 2009 onwards
    df_fcast = pd.DataFrame({"date": list(yvalues.index), "TSLA_fcast": forecasted})
    df_fcast = df_fcast.set_index("date")
    
    df = pd.merge(yvalues, df_fcast, left_index=True, right_index=True)

    df["TSLA_fcast"].plot(ax=ax, legend=True, linewidth=2.5, linestyle="dashed", color="forestgreen") # TSLA fitted
    df["TSLA_diff"].plot(ax=ax, legend=True, linewidth=1.5, linestyle="solid", color="salmon") # Actual TSLA values
    
    ax.set_title("TSLA vs. Model's TSLA")
    ax.set_ylabel("First differences")
    ax.legend(["Fitted TSLA","Actual TSLA"])

x_train = dset2.loc["2020-01-05":"2021-06-21", names2]
x_test = dset2.loc["2021-06-21":,names2]
y_train = dset2.loc["2020-01-05":"2021-06-21", "TSLA_diff"]
y_test = dset2.loc["2021-06-21":, "TSLA_diff"]

lasso = linear_model.LassoCV(cv=model_selection.TimeSeriesSplit(n_splits=5), 
                             alphas=None, tol = 10000, normalize=True) 

fred_lasso = lasso.fit(x_train, y_train)
optimal_alpha = fred_lasso.alpha_

lasso2 = linear_model.Lasso(alpha=optimal_alpha, normalize=True)
lasso2.fit(x_train, y_train)

lasso2.coef_
#train_test_plot(dset_EN, x_train, x_test) 

array([ 7.20902440e-02,  2.00701734e-02, -4.02847424e-01, -2.21122815e+00,
        3.77903319e-01, -6.91098494e-03, -3.34285652e-01,  4.24181205e-01,
        8.54914242e-02,  3.52091625e-02, -2.50758876e-02, -3.56472136e-02,
        3.52150559e+00,  6.06896275e-02,  8.61617708e-03,  7.33200359e-03,
        3.14226828e+00,  2.28882758e-04])

fig, ax = plt.subplots(figsize=(12,4))
colors = sns.color_palette("deep", 8)

yvalues = pd.DataFrame(y_test)
    
forecasted = list(lasso2.predict(x_test)) # Use the model fit on features data from 2009 onwards
df_fcast = pd.DataFrame({"date": list(yvalues.index), "TSLA_fcast": forecasted})
df_fcast = df_fcast.set_index("date")
    
df = pd.merge(yvalues, df_fcast, left_index=True, right_index=True)


df["TSLA_fcast"].plot(ax=ax, legend=True, linewidth=2.5, linestyle="dashed", color="forestgreen") # TSLA fitted
df["TSLA_diff"].plot(ax=ax, legend=True, linewidth=1.5, linestyle="solid", color="salmon") # Actual TSLA values
    
ax.set_title("TSLA vs. Model's TSLA")
ax.set_ylabel("First differences")
ax.legend(["Fitted TSLA","Actual TSLA"])

<matplotlib.legend.Legend at 0x272c414f5e0>

family_1

metrics.mean_squared_error(y_test, dset_EN.predict(x_test))

3.8741380753790273

lasso_coefs = pd.DataFrame({"features":list(x_train), "coef": lasso2.coef_})
lasso_coefs = lasso_coefs[lasso_coefs.coef != 0.0]
lasso_coefs.sort_values("coef", ascending=False)
features coef
12 Tether_diff 3.521506
16 USDC_diff 3.142268
7 XAG_diff 0.424181
4 10YBE_diff 0.377903
8 BTC_diff 0.085491
0 10CMR_diff 0.072090
13 XRP_diff 0.060690
9 ETH_diff 0.035209
1 FFR_diff 0.020070
14 SOL_diff 0.008616
15 pDOTn_diff 0.007332
17 DOGE_diff 0.000229
5 oil_diff -0.006911
10 BNB_diff -0.025076
11 ADA_diff -0.035647
6 XAU_diff -0.334286
2 infexp_diff -0.402847
3 TWD_diff -2.211228 
names3 = ["TSLA_diff","FFR_diff", "ETH_diff", "XRP_diff",\
          "10YBE_diff", "BTC_diff", "SOL_diff"]
dset3 = dset1.loc[:,names3]
#mse2, df2 = var_create(columns=names, data=dset)
#print(f"The mean squared error between the forecasted and actual values is {mse2}")

start_date = "2021-06-21"
end_date = "2021-10-19"

dset3.index.names = ["Date"]
dset3.index = pd.to_datetime(dset.index)
dset3.to_period("D")

data_train = dset3.loc["2020-01-02":"2021-06-21", :]
var_train = VAR(data_train)
results = var_train.fit(25)
lag_order = results.k_ar
forecasted = pd.DataFrame(results.forecast(data_train.values[-lag_order:], 120)) # Forecast 120 months

# Rename forecasted columns
forecasted_names = list(forecasted.columns.values)
data_train_names = list(data_train.columns.values)

var_dict = dict(zip(forecasted_names, data_train_names))
for f,t in var_dict.items():
    forecasted = forecasted.rename(columns={f:t + "_fcast"})
    
forecasted.index= pd.DatetimeIndex(pd.date_range(start_date, periods=forecasted.shape[0]))
forecasted.index.names = ["Date"]

# Parse together forecasted data with original dataset
final_data = pd.merge(forecasted, dset3, left_index=True, right_index=True)
final_data = final_data.sort_index(axis=0, ascending=True)
final_data = pd.concat([data_train, final_data], sort=True, axis=0)
final_data = final_data.sort_index(axis=0, ascending=True)

TSLA_fs = final_data.loc["2021-06-22":"2021-10-18","TSLA_diff_fcast"]
TSLA_r = final_data.loc["2021-06-22":"2021-10-18","TSLA_diff"]

print(TSLA_fs)
var_mse2 = metrics.mean_squared_error(TSLA_fs, TSLA_r)

Date
2021-06-22     9.055724
2021-06-23    12.795725
2021-06-24     0.255226
2021-06-25    -4.068157
2021-06-28    -1.563721
                ...    
2021-10-12    -0.436792
2021-10-13     0.067200
2021-10-14    -0.005382
2021-10-15     0.128331
2021-10-18    -0.751468
Name: TSLA_diff_fcast, Length: 83, dtype: float64

fig, ax = plt.subplots(figsize=(14,6))
colors = sns.color_palette("deep", 8)

TSLA_rplot = final_data.loc["2021-01-02":"2021-10-18","TSLA_diff"]

TSLA_fs.plot(ax=ax, legend=True, linewidth=2.5, linestyle="dashed")
TSLA_rplot.plot(ax=ax, legend=True, alpha=0.6, linestyle="solid")

ax.set_title("VAR in-sample forecast, LASSO approach", fontsize=16, fontweight="bold", fontname="Verdana", loc="left")
ax.set_ylabel("First differences", fontname="Verdana")
ax.legend([f"VAR Forecast, MSE={var_mse2}", "TSLA Real Fluctuations"])

<matplotlib.legend.Legend at 0x272c71231f0>

family_1

Result and inference

With the traditional approach, we can not find any significant coefficient relationship between the stock price of Tesla and the price of cryptocurrencies. However, with the LASSO, we figure out that even the coefficients of cryptocurrencies do not have statistical significance, the fluctuations of cryptocurrencies can support to explain more the change of stock price of Tesla because the MSE with the LASSO is lower than that with the traditional approach. Furthermore, we can confirm that even though the change of price of cryptocurrencies did not affect the fluctuations of the stock price of Tesla, nowadays the effect has become larger than before.

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