马尔可夫切换自回归模型¶

import requests
import shutil

def download_file(url):
    local_filename = url.split('/')[-1]
    with requests.get(url, stream=True) as r:
        with open(local_filename, 'wb') as f:
            shutil.copyfileobj(r.raw, f)

    return local_filename

filename = download_file("https://www.stata-press.com/data/r14/rgnp.dta")
# Get the RGNP data to replicate Hamilton

dta = pd.read_stata(filename).iloc[1:]
dta.index = pd.DatetimeIndex(dta.date, freq="QS")
dta_hamilton = dta.rgnp

# Plot the data
dta_hamilton.plot(title="Growth rate of Real GNP", figsize=(12, 3))

# Fit the model
mod_hamilton = sm.tsa.MarkovAutoregression(
    dta_hamilton, k_regimes=2, order=4, switching_ar=False
)
res_hamilton = mod_hamilton.fit()

res_hamilton.summary()

fig, axes = plt.subplots(2, figsize=(7, 7))
ax = axes[0]
ax.plot(res_hamilton.filtered_marginal_probabilities[0])
ax.fill_between(usrec.index, 0, 1, where=usrec["USREC"].values, color="k", alpha=0.1)
ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])
ax.set(title="Filtered probability of recession")

ax = axes[1]
ax.plot(res_hamilton.smoothed_marginal_probabilities[0])
ax.fill_between(usrec.index, 0, 1, where=usrec["USREC"].values, color="k", alpha=0.1)
ax.set_xlim(dta_hamilton.index[4], dta_hamilton.index[-1])
ax.set(title="Smoothed probability of recession")

fig.tight_layout()

print(res_hamilton.expected_durations)

# Get the dataset
ew_excs = requests.get("http://econ.korea.ac.kr/~cjkim/MARKOV/data/ew_excs.prn").content
raw = pd.read_table(BytesIO(ew_excs), header=None, skipfooter=1, engine="python")
raw.index = pd.date_range("1926-01-01", "1995-12-01", freq="MS")

dta_kns = raw.loc[:"1986"] - raw.loc[:"1986"].mean()

# Plot the dataset
dta_kns[0].plot(title="Excess returns", figsize=(12, 3))

# Fit the model
mod_kns = sm.tsa.MarkovRegression(
    dta_kns, k_regimes=3, trend="n", switching_variance=True
)
res_kns = mod_kns.fit()

res_kns.summary()

fig, axes = plt.subplots(3, figsize=(10, 7))

ax = axes[0]
ax.plot(res_kns.smoothed_marginal_probabilities[0])
ax.set(title="Smoothed probability of a low-variance regime for stock returns")

ax = axes[1]
ax.plot(res_kns.smoothed_marginal_probabilities[1])
ax.set(title="Smoothed probability of a medium-variance regime for stock returns")

ax = axes[2]
ax.plot(res_kns.smoothed_marginal_probabilities[2])
ax.set(title="Smoothed probability of a high-variance regime for stock returns")

fig.tight_layout()

# Get the dataset
filardo = requests.get("http://econ.korea.ac.kr/~cjkim/MARKOV/data/filardo.prn").content
dta_filardo = pd.read_table(
    BytesIO(filardo), sep=" +", header=None, skipfooter=1, engine="python"
)
dta_filardo.columns = ["month", "ip", "leading"]
dta_filardo.index = pd.date_range("1948-01-01", "1991-04-01", freq="MS")

dta_filardo["dlip"] = np.log(dta_filardo["ip"]).diff() * 100
# Deflated pre-1960 observations by ratio of std. devs.
# See hmt_tvp.opt or Filardo (1994) p. 302
std_ratio = (
    dta_filardo["dlip"]["1960-01-01":].std() / dta_filardo["dlip"][:"1959-12-01"].std()
)
dta_filardo.loc[:"1959-12-01", "dlip"] = dta_filardo["dlip"][:"1959-12-01"] * std_ratio

dta_filardo["dlleading"] = np.log(dta_filardo["leading"]).diff() * 100
dta_filardo["dmdlleading"] = dta_filardo["dlleading"] - dta_filardo["dlleading"].mean()

# Plot the data
dta_filardo["dlip"].plot(
    title="Standardized growth rate of industrial production", figsize=(13, 3)
)
plt.figure()
dta_filardo["dmdlleading"].plot(title="Leading indicator", figsize=(13, 3))

res_filardo.summary()

fig, ax = plt.subplots(figsize=(12, 3))

ax.plot(res_filardo.smoothed_marginal_probabilities[0])
ax.fill_between(usrec.index, 0, 1, where=usrec["USREC"].values, color="gray", alpha=0.2)
ax.set_xlim(dta_filardo.index[6], dta_filardo.index[-1])
ax.set(title="Smoothed probability of a low-production state")

res_filardo.expected_durations[0].plot(
    title="Expected duration of a low-production state", figsize=(12, 3)
)