목표

앞말

브리지 방정식

y_t = \alpha + \sum_{i=1}^{N} \beta_i x^Q_{i,t} + \varepsilon _t \\
x^Q_{i,t} = \frac{1}{3}(x^M_{i,3t} + 2 x^M_{i,3t-1} + 3 x^M_{i,3t-2} + 2 x^M_{i,3t-3} + x^M_{i,3t-4})

# ブリッジ方程式モデル(単回帰分析)
df4 = pd.merge(gdp, iip, left_index=True, right_index=True, how='outer')
df5 = pd.DataFrame(columns=['BRIDGE'])

x = np.array([])
flag = False
for date, IIP_YOY in zip(df4.index, df4['IIP_YOY']):

    x = np.append(x, IIP_YOY)
    if flag == False:
        if date == '2013-07-01':
            flag = True

    if flag:
        x3t = x[-1]
        x3tm1 = x[-2]
        x3tm2 = x[-3]
        x3tm3 = x[-4]
        x3tm4 = x[-5]
        xt = (x3t + 2*x3tm1 + 3*x3tm2 + 2*x3tm3 + x3tm4)/3
        record = pd.Series([xt],
                           index=df5.columns, name=date)
        df5 = df5.append(record)

df5.index.name = 'DATE'
df6 = pd.merge(df4, df5, left_index=True, right_index=True, how='outer')
df6 = df6.dropna()

# 目的変数(Y)、説明変数(X)
Y2 = df6['GDP_CYOY']
X2 = df6[['BRIDGE']]

# 線形回帰をする
model = linear_model.LinearRegression()
model.fit(X2, Y2)

# パラメータ算出
reg_a = model.coef_[0]
reg_b = model.intercept_

df6['NOWCAST'] = df6.apply(lambda x: reg_b + reg_a*x['BRIDGE'], axis=1)

MIDAS

y_t = \alpha + \sum_{i=1}^{K} \sum_{j=0}^{l_i} \beta_{i,j} x^M_{i,3t - j} + \varepsilon _t

# 日本の会計年度が4月始まりのため、4月を起点としている。
df['period'] = pd.to_datetime(df.index.to_series()).apply(
    lambda x: 3 if x.month in [1, 4, 7, 10] else (1 if x.month in [2, 5, 8, 11] else 2))

df = df[df.index != '2013-01-01']

df2 = pd.DataFrame(columns=[
                   'GDP_CYOY', 'IIP_YOY_Q1', 'IIP_YOY_Q2', 'IIP_YOY_Q3'])
for date, GDP_CYOY, IIP_YOY, period in zip(df.index, df.GDP_CYOY, df.IIP_YOY, df.period):

    if period == 1:
        q1 = IIP_YOY
    elif period == 2:
        q2 = IIP_YOY
    else:
        record = pd.Series([GDP_CYOY, q1, q2, IIP_YOY],
                           index=df2.columns, name=date)
        df2 = df2.append(record)

df2.index.name = 'DATE'


# 目的変数(Y)、説明変数(X)
Y = np.array(df2['GDP_CYOY'])
X = np.array(df2[['IIP_YOY_Q1', 'IIP_YOY_Q2', 'IIP_YOY_Q3']])

# 予測モデルを作成
clf.fit(X, Y)

# 偏回帰係数
ab = pd.DataFrame({"Name": ['IIP_YOY_Q1', 'IIP_YOY_Q2', 'IIP_YOY_Q3'],
                  "Coefficients": clf.coef_}).sort_values(by='Coefficients')
for index, row in ab.iterrows():
    if row.Name == 'IIP_YOY_Q3':
        b3 = row.Coefficients
    elif row.Name == 'IIP_YOY_Q2':
        b2 = row.Coefficients
    else:
        b1 = row.Coefficients
# 切片
print(clf.intercept_)
a = clf.intercept_

df2['NOWCAST'] = df2.apply(lambda x: a + b1*x['IIP_YOY_Q1'] +
                           b2*x['IIP_YOY_Q2'] + b3*x['IIP_YOY_Q3'], axis=1)

참고 문헌