def harmonic_fit_mcmc_arn(time, X, frq, arn=1, mask=None, axis=0, basetime=None, **kwargs):
"""
Harmonic fitting using Bayesian inference
Model the errors using an auto-regressive model
"""
tday = 86400.
# Convert the time to days
dtime = SecondsSince(time, basetime=basetime )
nt = dtime.shape[0]
dtime /= tday
# Convert the frequencies to radians / day
omega = [ff*tday for ff in frq]
#omega = frq
# Number of parameters
n_params = 2*len(omega) + 1
print('Number of Parametrs: %d\n'%n_params, omega)
with pm.Model() as my_model:
###
# Create priors for each of our variables
BoundNormal = pm.Bound(pm.Normal, lower=0.0)
# Mean
beta_mean = pm.Normal('beta_mean', mu=0, sd=1)
beta_s=[beta_mean]
# Harmonics
for n in range(0,2*len(omega),2):
beta_s.append(pm.Normal('beta_%d_re'%(n//2), mu=1., sd = 5.))
beta_s.append(pm.Normal('beta_%d_im'%(n//2), mu=1., sd = 5.))
###
# Generate the likelihood function using the deterministic variable as the mean
mu_x = sine_model_notrend(beta_s, omega, dtime)
# Use an autoregressive model for the error term
beta = pm.Normal('beta', mu=0, sigma=1., shape=arn)
#sigma = pm.InverseGamma('sigma',1,1)
sigma = pm.HalfNormal('sigma',1)
X_obs = pm.AR('X_obs', beta, sigma=sigma, observed=X - mu_x)
# Inference step...
step = None
start = None
trace = pm.sample(500, tune=1000, start = start, step=step, cores=2,
return_inferencedata=False)#nuts_kwargs=dict(target_accept=0.95, max_treedepth=16, k=0.5))
# Return the trace and the parameter stats
return trace, my_model, omega, dtime
def ar_model_pred_advi_dynamic(X, ar_order):
# prepare training dataset
train_size = int(X.shape[0] * 0.66)
train, test = X.iloc[0:train_size], X.iloc[train_size:]
history = [x for x in train]
# make predictions
predictions = list()
for t in range(test.shape[0]):
tau = 0.001
model = pm.Model()
with model:
beta = pm.Uniform('beta', lower=-1, upper=1, shape=ar_order)
y_obs = pm.AR('y_obs', rho=beta, tau=tau, observed=history)
#trace = pm.sample(2000, tune=1000)
step = step = pm.ADVI()
n_draws, n_chains = 3000, 3
n_sim = n_draws * n_chains
advi_fit = pm.fit(method=pm.ADVI(), n=30000)
# Consider 3000 draws and 2 chains.
advi_trace = advi_fit.sample(10000)
values = history[len(history) - ar_order:]
values = values[::-1]
yhat = np.dot(get_coef_from_trace(advi_trace), values)
predictions.append(yhat)
history.append(test[t])
history = history[1:]
# calculate out of sample error
#error = mean_squared_error(test, predictions)
predictions = pd.DataFrame(predictions)
predictions.set_index(X[train_size:X.shape[0]].index,
inplace=True,
drop=True)
return predictions[0]
jpfont = FontProperties(fname=FontPath)
#%% ノイズを含むAR(1)過程からデータを生成
n = 500
np.random.seed(99)
x = np.empty(n)
x[0] = st.norm.rvs() # 定常分布の分散 = 0.19/(1 - 0.9**2) = 1.0
for t in range(1, n):
x[t] = 0.9 * x[t-1] + st.norm.rvs(scale=np.sqrt(0.19))
y = x + st.norm.rvs(scale=0.5, size=n)
#%% 事後分布の設定
ar1_model = pm.Model()
with ar1_model:
sigma = pm.HalfCauchy('sigma', beta=1.0)
rho = pm.Uniform('rho', lower=-1.0, upper=1.0)
omega = pm.HalfCauchy('omega', beta=1.0)
ar1 = pm.AR('ar1', rho, sigma=omega, shape=n,
init=pm.Normal.dist(sigma=omega/pm.math.sqrt(1 - rho**2)))
observation = pm.Normal('y', mu=ar1, sigma=sigma, observed=y)
#%% 事後分布からのサンプリング
n_draws = 5000
n_chains = 4
n_tune = 1000
with ar1_model:
trace = pm.sample(draws=n_draws, chains=n_chains, tune=n_tune,
random_seed=123)
param_names = ['sigma', 'rho', 'omega']
print(pm.summary(trace, var_names=param_names))
#%% 事後分布のグラフの作成
labels = ['$\\sigma$', '$\\rho$', '$\\omega$']
k = len(labels)
fig, ax = plt.subplots(k, 2, num=1, figsize=(8, 1.5*k), facecolor='w')
for index in range(k):
http://fx.sauder.ubc.ca/data.html
"""
data = pd.read_csv('dollaryen.csv', index_col=0)
y = 100 * np.diff(np.log(data.values.ravel()))
n = y.size
series_date = pd.to_datetime(data.index[1:])
#%% SVモデルの設定
sv_model = pm.Model()
with sv_model:
nu = pm.Exponential('nu', 0.2)
sigma = pm.HalfCauchy('sigma', beta=1.0)
rho = pm.Uniform('rho', lower=-1.0, upper=1.0)
omega = pm.HalfCauchy('omega', beta=1.0)
log_vol = pm.AR('log_vol',
rho,
sd=omega,
shape=n,
init=pm.Normal.dist(sd=omega / pm.math.sqrt(1 - rho**2)))
observation = pm.StudentT('y',
nu,
sd=sigma * pm.math.exp(log_vol),
observed=y)
#%% 事後分布からのサンプリング
n_draws = 5000
n_chains = 4
n_tune = 2000
with sv_model:
trace = pm.sample(draws=n_draws,
chains=n_chains,
tune=n_tune,
random_seed=123,
http://www.fepc.or.jp/library/data/tokei/index.html
"""
data = pd.read_csv('electricity.csv', index_col=0)
y0 = np.log(data.values.reshape((data.shape[0]//3, 3)).sum(axis=1))
y = 100 * (y0 - y0[0])
n = y.size
series_date = pd.date_range(start='1/1/1989', periods=n, freq='Q')
#%% 確率的トレンド+季節変動
trend_coef = np.array([2.0, -1.0])
seasonal_coef = np.array([-1.0, -1.0, -1.0])
timeseries_decomp = pm.Model()
with timeseries_decomp:
sigma = pm.HalfCauchy('sigma', beta=1.0)
tau = pm.HalfCauchy('tau', beta=1.0)
omega = pm.HalfCauchy('omega', beta=1.0)
trend = pm.AR('trend', trend_coef, sigma=tau, shape=n)
seasonal = pm.AR('seasonal', seasonal_coef, sigma=omega, shape=n)
observation = pm.Normal('y', mu=trend+seasonal, sigma=sigma, observed=y)
#%% 事後分布からのサンプリング
n_draws = 5000
n_chains = 4
n_tune = 2000
with timeseries_decomp:
trace = pm.sample(draws=n_draws, chains=n_chains, tune=n_tune,
target_accept=0.95, random_seed=123)
param_names = ['sigma', 'tau', 'omega']
print(pm.summary(trace, var_names=param_names))
#%% 事後分布のグラフの作成
series_name = ['原系列', '平滑値', 'トレンド', '季節変動', 'ノイズ']
labels = ['$\\sigma$', '$\\tau$', '$\\omega$']
k = len(labels)
#
# clark_sigmaT = np.mean(trace['sigmaT'])
# clark_mu = np.mean(trace['mu'])
#
# print "Clark (1973) model parameters:"
# print "SigmaT = ", clark_sigmaT
# print "Mu = ", clark_mu
clark_sigmaT = 0.57
clark_mu = -4.91
with pm.Model() as taylor_model:
sigmaT = pm.Uniform('sigmaT', lower=0.001, upper=.2, testval=0.05)
rhos = pm.Uniform('rhos', lower=-1., upper=1., shape=5)
mu = pm.Uniform('mu', lower=-7., upper=-3., testval=-5.)
time_process = pm.AR('time_process', rho=rhos, sd=sigmaT, shape=N)
pm.Normal('obs',
mu=0.,
sd=pm.math.exp(mu + time_process),
observed=returns)
mean_field = pm.fit(30000,
method='advi',
obj_optimizer=pm.adam(learning_rate=0.01))
trace = mean_field.sample(1000)
taylor_sigmaT = np.mean(trace['sigmaT'])
taylor_mu = np.mean(trace['mu'])
taylor_rhos = np.mean(trace['rhos'], axis=0)
