def forecast_ts_arima(self, returns, model, order, days=21):
# create an n-day forecast of returns with 95%, 99% CI
f, err95, ci95 = model.forecast(steps=days, alpha=0.05) # 95% CI
_, err99, ci99 = model.forecast(steps=days, alpha=0.01) # 99% CI
# generate date index for next n-days excluding last day of returns
idx = pd.date_range(data.index[-1], periods=days, freq='D')
# reconstruct the forecast into dataframe
fc_95 = pd.DataFrame(
np.column_stack([f, ci95]),
index=idx,
columns=['forecast', 'lower_ci_95', 'upper_ci_95']
)
fc_99 = pd.DataFrame(
np.column_stack([ci99]),
index=idx,
columns=['lower_ci_99', 'upper_ci_99']
)
fc_all = fc_95.combine_first(fc_99)
logn(fc_all.head())
# get the returns for last sample days, say 500 days
sample_days = 500
ts = returns.iloc[-sample_days:].copy()
# get the sample prediction over last sample days
pred = model.predict(ts.index[0], ts.index[-1])
# construct the title and file name
title = '{} Day Returns Forecast\nARIMA{}'.format(days, order)
filename = 'ts_forecast_arima{}{}{}.png'.format(
order[0], order[1], order[2]
)
# do the plotting
self.g.fcplot(ts, pred, fc_all, title, filename)
def __construct_web_url(self, scrip_code, start_date, end_date):
# components of the URL
protocol = 'https://'
host_name = 'query2.finance.yahoo.com'
path_fmt = '/v8/finance/chart/{}'
params_fmt = '?formatted={}&crumb={}&lang={}®ion={}&period1={}&' + \
'period2={}&interval={}&events={}&corsDomain={}'
# constant initializations needed in the URL
formatted = True
crumb = '4D5ubVRDG3o'
lang = 'en-IN'
region = 'IN'
period1 = DateTime.seconds_from_date(start_date)
period2 = DateTime.seconds_from_date(end_date)
interval = '1d'
events = 'div%7Csplit'
corsDomain = 'in.finance.yahoo.com'
# populate the path and other parameters using the computed values
filled_path = path_fmt.format(quote(scrip_code))
filled_params = params_fmt.format(formatted, crumb, lang, region,
period1, period2, interval, events,
corsDomain)
# constructing the complete url for GET request
web_url = protocol + host_name + filled_path + filled_params
logn('=' * 40)
logn(web_url)
logn('-' * 20)
logn('Looking for ({}) from {} till {}...[Done]'.format(
scrip_code, start_date, end_date))
return web_url
def analyse_arma_p_q(self, p=1, q=1):
n = self.__n_samples
burns = n // 10
a, b, rts = self.get_sample_data(
m=SerialCorrelation.ModelType.arma, p=p, q=q, n=n, b=burns
)
self.g.tsplot(rts,
lags=self.__n_lags,
saveas='arma{}{}.png'.format(p, q)
)
try:
ar_p, ar_o, ma_p, ma_o = self.fit_arma_model_and_estimate_order(
rts, maxlag=10, order=(p, q),
method='mle', trend='nc', burnin=burns
)
logn('alpha estimate: {} | best ar lag order = {}'
.format(ar_p, ar_o))
logn('beta estimate: {} | best ma lag order = {}'
.format(ma_p, ma_o))
except ValueError:
pass
logn('true alphas = {} | true ar order = {}'
.format(a, p))
logn('true betas = {} | true ma order = {}'
.format(b, q))
def fit_arma_model_and_estimate_order(
self, data, order=(0, 1), maxlag=None,
method='mle', trend='nc', burnin=0
):
if maxlag is None:
maxlag = self.__n_lags
log('Fitting & estimating the ARMA model to the given data...')
mdl = smt.ARMA(data, order=order).fit(
maxlag=maxlag,
method=method,
trend=trend,
burnin=burnin
)
logn('[Done]')
logn(mdl.summary())
return mdl.arparams, mdl.k_ar, mdl.maparams, mdl.k_ma
def __fetch_and_parse_json(self, web_url: str):
log('Fetching financial data from Yahoo Finance...')
# query the web server at URL and return the JSON response
web_request = requests.get(web_url)
web_response = web_request.text
# get hold of respective fields
json_obj = json.loads(web_response)
timestamp = json_obj['chart']['result'][0]['timestamp']
indicators = json_obj['chart']['result'][0]['indicators']
opened = indicators['quote'][0]['open']
high = indicators['quote'][0]['high']
low = indicators['quote'][0]['low']
closed = indicators['quote'][0]['close']
volume = indicators['quote'][0]['volume']
adjclosed = indicators['adjclose'][0]['adjclose']
logn('[Done]')
log('Parsing the json response...')
fin_data = []
headers = [
'Date', 'Open', 'High', 'Low', 'Close', 'Adjusted Close', 'Volume'
]
# extract information of each field and keep in a list of lists
for index in range(len(timestamp)):
if opened[index] is None or high[index] is None or \
low[index] is None or closed[index] is None or \
volume[index] is None or adjclosed[index] is None:
continue
data = []
data.append(DateTime.date_string_from_seconds(timestamp[index]))
data.append(opened[index])
data.append(high[index])
data.append(low[index])
data.append(closed[index])
data.append(adjclosed[index])
data.append(volume[index])
fin_data.append(data)
df = pd.DataFrame(fin_data, columns=headers)
# replacing zeros with respective avg so that they can be handled later
df = df[headers].replace({'0': np.nan, 0: np.nan})
# ignore date column for mean calculations
headers = headers[1:]
# replace NaN in each column with respective column mean
for header in headers:
df[header].fillna(df[header].mean(), inplace=True)
logn('[Done]')
if self.__save_mode:
log('Exporting the data to CSV file...')
# save as a CSV file
csv_path = self.__csv_path
df.to_csv(csv_path, index=False, encoding='utf-8')
logn('[Done]')
logn('Saved file: {}'.format(csv_path))
# parse Date column as python datetime
df.Date = df.Date.apply(DateTime.dateparser_short)
# re-index the dataframe on converted Date column
df.set_index('Date', drop=True, inplace=True)
return df
def analyse_ma_q(self, q=1):
a, b, rts = self.get_sample_data(
m=SerialCorrelation.ModelType.ma, q=q
)
self.g.tsplot(rts,
lags=self.__n_lags,
saveas='ma{}.png'.format(q)
)
try:
_, _, params, order = self.fit_arma_model_and_estimate_order(
rts, maxlag=10, order=(0, q), method='mle', trend='nc'
)
logn('beta estimate: {} | best lag order = {}'
.format(params, order))
except ValueError:
pass
true_order = q
logn('true betas = {} | true order = {}'
.format(b, true_order))
def analyse_ar_1_with_root(self, a=1.0):
assert a != 0.0, 'AR root can not be zero'
assert a < 1.0, 'AR root can not be greater than one'
np.random.seed(self.seed)
x = w = np.random.normal(size=self.__n_samples)
for t in range(1, self.__n_samples):
x[t] = a * x[t-1] + w[t]
self.g.tsplot(
x,
lags=self.__n_lags,
saveas='ar1_{:04.2f}.png'.format(a)
)
# our simulated AR model has order = 1 with alpha = 0.6
# if we fit an AR(p) model to the above simulated data and ask it to
# select the order, the selected values of p and a should match with
# the actual ones
params, order = self.fit_ar_model_and_estimate_order(x)
true_order = 1
logn('alpha estimate: {:3.2f} | best lag order = {}'
.format(params[0], order))
logn('true alpha = {:3.2f} | true order = {}'
.format(a, true_order))
def fit_ar_model_and_estimate_order(
self, data, maxlag=None, method='mle', ic='bic', trend='nc'
):
if maxlag is None:
maxlag = self.__n_lags
log('Fitting the AR model to the given data...')
mdl = smt.AR(data).fit(
maxlag=maxlag,
method=method,
ic=ic,
trend=trend
)
logn('[Done]')
log('Estimating the order of the AR model...')
est_order = smt.AR(data).select_order(
maxlag=maxlag,
method=method,
ic=ic,
trend=trend
)
logn('[Done]')
return mdl.params, est_order
def analyse_ts_log_returns_as_ar_process(self, data):
logged = self.__logged_data(data)
self.g.tsplot(
logged.Close,
lags=self.__n_lags,
saveas='ts_log_returns.png'
)
logn('BIC', '='*20, sep='\n')
params, order = self.fit_ar_model_and_estimate_order(
logged.Close, maxlag=10, method='mle', ic='bic', trend='nc'
)
if order is 1:
logn('alpha estimate: {:.5f} | best lag order = {}'
.format(params[0], order))
else:
logn('alpha estimate: {} | best lag order = {}'
.format(params, order))
def analyse_ts_arima(self, data):
ts = data.LSPY
best_ic = np.inf
best_order = None
best_mdl = None
pq_rng = range(5) # orders greater than 5 are not practically useful
d_rng = range(2) # [0,1]
for i in pq_rng:
for d in d_rng:
for j in pq_rng:
try:
tmp_mdl = smt.ARIMA(ts, order=(i, d, j)).fit(
method='mle', trend='nc'
)
tmp_ic = tmp_mdl.aic # using aic here
logn('ic={}, order=({}, {}, {})'.format(tmp_ic,i,d,j))
if tmp_ic < best_ic:
best_ic = tmp_ic
best_order = (i, d, j)
best_mdl = tmp_mdl
except: continue
logn(best_mdl.summary())
logn('using AIC', '='*20, sep='\n')
logn('ic: {:6.5f} | estimated order: {}'.format(best_ic, best_order))
logn('estimated alphas = {}'.format(best_mdl.arparams))
logn('estimated betas = {}'.format(best_mdl.maparams))
self.g.tsplot(best_mdl.resid,
lags=self.__n_lags,
saveas='ts_arima{}{}{}_residuals.png'.format(
best_order[0], best_order[1], best_order[2]
)
)
# forecasting on the basis of best fit arima model
self.forecast_ts_arima(ts, best_mdl, best_order) # ts should have index
def analyse_ts_arma(self, data):
ts = self.__logged_data(data).Close
best_ic = np.inf
best_order = None
best_mdl = None
rng = range(5) # orders greater than 5 are not practically useful
for i in rng:
for j in rng:
try:
tmp_mdl = smt.ARMA(ts, order=(i, j)).fit(
method='mle', trend='nc'
)
tmp_ic = tmp_mdl.bic # using bic here
logn('ic={}, order=({}, {})'.format(tmp_ic, i, j))
if tmp_ic < best_ic:
best_ic = tmp_ic
best_order = (i, j)
best_mdl = tmp_mdl
except: continue
logn(best_mdl.summary())
logn('using BIC', '='*20, sep='\n')
logn('ic: {:6.5f} | estimated order: {}'.format(best_ic, best_order))
logn('estimated alphas = {}'.format(best_mdl.arparams))
logn('estimated betas = {}'.format(best_mdl.maparams))
self.g.tsplot(best_mdl.resid,
lags=self.__n_lags,
saveas='ts_arma{}{}_residuals.png'.format(
best_order[0], best_order[1]
)
)
def analyse_arma_p_q_best_ic(self, p=1, q=1):
n = 5000
burns = 2000
a, b, rts = self.get_sample_data(
m=SerialCorrelation.ModelType.arma, p=p, q=q, n=n, b=burns
)
self.g.tsplot(rts,
lags=self.__n_lags,
saveas='arma{}{}.png'.format(p, q)
)
# pick best order by minimum ic - aic or bic
# smallest ic value wins
best_ic = np.inf
best_order = None
best_mdl = None
rng = range(5)
for i in rng:
for j in rng:
try:
tmp_mdl = smt.ARMA(rts, order=(i, j)).fit(
method='mle', trend='nc'
)
tmp_ic = tmp_mdl.bic # using bic here
if tmp_ic < best_ic:
best_ic = tmp_ic
best_order = (i, j)
best_mdl = tmp_mdl
except: continue
logn(best_mdl.summary())
logn('using BIC', '='*20, sep='\n')
logn('true order: ({}, {})'.format(p, q))
logn('true alphas = {}'.format(a))
logn('true betas = {}'.format(b))
logn('ic: {:6.5f} | estimated order: {}'.format(best_ic, best_order))
logn('estimated alphas = {}'.format(best_mdl.arparams))
logn('estimated betas = {}'.format(best_mdl.maparams))
# analysing the model residuals with the estimated information
# the residuals should be a white noise process with no serial
# correlation for any lag, if this is the case then we can say
# that the best model has been fit to explain the data
self.g.tsplot(best_mdl.resid,
lags=self.__n_lags,
saveas='arma{}{}_residuals.png'.format(
best_order[0], best_order[1]
)
)
def analyse_ar_p(self, p=1):
a, b, rts = self.get_sample_data(
m=SerialCorrelation.ModelType.ar, p=p
)
self.g.tsplot(rts,
lags=self.__n_lags,
saveas='ar{}.png'.format(p)
)
logn('AIC', '='*20, sep='\n')
params, order = self.fit_ar_model_and_estimate_order(
rts, maxlag=10, method='mle', ic='aic', trend='nc'
)
true_order = p
logn('alpha estimate: {} | best lag order = {}'
.format(params, order))
logn('true alphas = {} | true order = {}'
.format(a, true_order))
logn()
logn('BIC', '='*20, sep='\n')
params, order = self.fit_ar_model_and_estimate_order(
rts, maxlag=10, method='mle', ic='bic', trend='nc'
)
true_order = p
logn('alpha estimate: {} | best lag order = {}'
.format(params, order))
logn('true alphas = {} | true order = {}'
.format(a, true_order))