【2.6.1】时间序列图(Time Series Plot)

时间序列图用于显示给定度量随时间变化的方式。 在这里,您可以看到1949年至1969年间航空客运量的变化情况。

# Import Data
df = pd.read_csv('https://github.com/selva86/datasets/raw/master/AirPassengers.csv')

# Draw Plot
plt.figure(figsize=(16,10), dpi= 80)
plt.plot('date', 'traffic', data=df, color='tab:red')

# Decoration
plt.ylim(50, 750)
xtick_location = df.index.tolist()[::12]
xtick_labels = [x[-4:] for x in df.date.tolist()[::12]]
plt.xticks(ticks=xtick_location, labels=xtick_labels, rotation=0, fontsize=12, horizontalalignment='center', alpha=.7)
plt.yticks(fontsize=12, alpha=.7)
plt.title("Air Passengers Traffic (1949 - 1969)", fontsize=22)
plt.grid(axis='both', alpha=.3)

# Remove borders
plt.gca().spines["top"].set_alpha(0.0)    
plt.gca().spines["bottom"].set_alpha(0.3)
plt.gca().spines["right"].set_alpha(0.0)    
plt.gca().spines["left"].set_alpha(0.3)   
plt.show()

二、带有峰和谷的时间序列注释 Time Series with Peaks and Troughs Annotated

下面的时间序列绘制了所有峰值和谷值,并注释了所选特殊事件的发生。

# Import Data
df = pd.read_csv('https://github.com/selva86/datasets/raw/master/AirPassengers.csv')

# Get the Peaks and Troughs
data = df['traffic'].values
doublediff = np.diff(np.sign(np.diff(data)))
peak_locations = np.where(doublediff == -2)[0] + 1

doublediff2 = np.diff(np.sign(np.diff(-1*data)))
trough_locations = np.where(doublediff2 == -2)[0] + 1

# Draw Plot
plt.figure(figsize=(16,10), dpi= 80)
plt.plot('date', 'traffic', data=df, color='tab:blue', label='Air Traffic')
plt.scatter(df.date[peak_locations], df.traffic[peak_locations], marker=mpl.markers.CARETUPBASE, color='tab:green', s=100, label='Peaks')
plt.scatter(df.date[trough_locations], df.traffic[trough_locations], marker=mpl.markers.CARETDOWNBASE, color='tab:red', s=100, label='Troughs')

# Annotate
for t, p in zip(trough_locations[1::5], peak_locations[::3]):
    plt.text(df.date[p], df.traffic[p]+15, df.date[p], horizontalalignment='center', color='darkgreen')
    plt.text(df.date[t], df.traffic[t]-35, df.date[t], horizontalalignment='center', color='darkred')

# Decoration
plt.ylim(50,750)
xtick_location = df.index.tolist()[::6]
xtick_labels = df.date.tolist()[::6]
plt.xticks(ticks=xtick_location, labels=xtick_labels, rotation=90, fontsize=12, alpha=.7)
plt.title("Peak and Troughs of Air Passengers Traffic (1949 - 1969)", fontsize=22)
plt.yticks(fontsize=12, alpha=.7)

# Lighten borders
plt.gca().spines["top"].set_alpha(.0)
plt.gca().spines["bottom"].set_alpha(.3)
plt.gca().spines["right"].set_alpha(.0)
plt.gca().spines["left"].set_alpha(.3)

plt.legend(loc='upper left')
plt.grid(axis='y', alpha=.3)
plt.show()

三、时间序列分解图 Time Series Decomposition Plot

时间序列分解图显示时间序列分解为趋势,季节和残差分量。

from statsmodels.tsa.seasonal import seasonal_decompose
from dateutil.parser import parse

# Import Data
df = pd.read_csv('https://github.com/selva86/datasets/raw/master/AirPassengers.csv')
dates = pd.DatetimeIndex([parse(d).strftime('%Y-%m-01') for d in df['date']])
df.set_index(dates, inplace=True)

# Decompose 
result = seasonal_decompose(df['traffic'], model='multiplicative')

# Plot
plt.rcParams.update({'figure.figsize': (10,10)})
result.plot().suptitle('Time Series Decomposition of Air Passengers')
plt.show()

四、Multiple Time Series

您可以绘制多个时间序列,在同一图表上测量相同的值,如下所示。

# Import Data
df = pd.read_csv('https://github.com/selva86/datasets/raw/master/mortality.csv')

# Define the upper limit, lower limit, interval of Y axis and colors
y_LL = 100
y_UL = int(df.iloc[:, 1:].max().max()*1.1)
y_interval = 400
mycolors = ['tab:red', 'tab:blue', 'tab:green', 'tab:orange']    

# Draw Plot and Annotate
fig, ax = plt.subplots(1,1,figsize=(16, 9), dpi= 80)    

columns = df.columns[1:]  
for i, column in enumerate(columns):    
    plt.plot(df.date.values, df.values, lw=1.5, color=mycolors[i])    
    plt.text(df.shape[0]+1, df.values[-1], column, fontsize=14, color=mycolors[i])

# Draw Tick lines  
for y in range(y_LL, y_UL, y_interval):    
    plt.hlines(y, xmin=0, xmax=71, colors='black', alpha=0.3, linestyles="--", lw=0.5)

# Decorations    
plt.tick_params(axis="both", which="both", bottom=False, top=False,    
                labelbottom=True, left=False, right=False, labelleft=True)        

# Lighten borders
plt.gca().spines["top"].set_alpha(.3)
plt.gca().spines["bottom"].set_alpha(.3)
plt.gca().spines["right"].set_alpha(.3)
plt.gca().spines["left"].set_alpha(.3)

plt.title('Number of Deaths from Lung Diseases in the UK (1974-1979)', fontsize=22)
plt.yticks(range(y_LL, y_UL, y_interval), [str(y) for y in range(y_LL, y_UL, y_interval)], fontsize=12)    
plt.xticks(range(0, df.shape[0], 12), df.date.values[::12], horizontalalignment='left', fontsize=12)    
plt.ylim(y_LL, y_UL)    
plt.xlim(-2, 80)    
plt.show()

五、Plotting with different scales using secondary Y axis

如果要显示在同一时间点测量两个不同数量的两个时间序列,则可以在右侧的辅助Y轴上再绘制第二个系列。

# Import Data
df = pd.read_csv("https://github.com/selva86/datasets/raw/master/economics.csv")

x = df['date']
y1 = df['psavert']
y2 = df['unemploy']

# Plot Line1 (Left Y Axis)
fig, ax1 = plt.subplots(1,1,figsize=(16,9), dpi= 80)
ax1.plot(x, y1, color='tab:red')

# Plot Line2 (Right Y Axis)
ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis
ax2.plot(x, y2, color='tab:blue')

# Decorations
# ax1 (left Y axis)
ax1.set_xlabel('Year', fontsize=20)
ax1.tick_params(axis='x', rotation=0, labelsize=12)
ax1.set_ylabel('Personal Savings Rate', color='tab:red', fontsize=20)
ax1.tick_params(axis='y', rotation=0, labelcolor='tab:red' )
ax1.grid(alpha=.4)

# ax2 (right Y axis)
ax2.set_ylabel("# Unemployed (1000's)", color='tab:blue', fontsize=20)
ax2.tick_params(axis='y', labelcolor='tab:blue')
ax2.set_xticks(np.arange(0, len(x), 60))
ax2.set_xticklabels(x[::60], rotation=90, fontdict={'fontsize':10})
ax2.set_title("Personal Savings Rate vs Unemployed: Plotting in Secondary Y Axis", fontsize=22)
fig.tight_layout()
plt.show()

六、Time Series with Error Bands

如果您有一个时间序列数据集,每个时间点(日期/时间戳)有多个观测值,则可以构建带有误差带的时间序列。 您可以在下面看到一些基于每天不同时间订单的示例。 另一个关于45天持续到达的订单数量的例子。

在该方法中,订单数量的平均值由白线表示。 并且计算95%置信带并围绕均值绘制。

from scipy.stats import sem

# Import Data
df = pd.read_csv("https://raw.githubusercontent.com/selva86/datasets/master/user_orders_hourofday.csv")
df_mean = df.groupby('order_hour_of_day').quantity.mean()
df_se = df.groupby('order_hour_of_day').quantity.apply(sem).mul(1.96)

# Plot
plt.figure(figsize=(16,10), dpi= 80)
plt.ylabel("# Orders", fontsize=16)  
x = df_mean.index
plt.plot(x, df_mean, color="white", lw=2) 
plt.fill_between(x, df_mean - df_se, df_mean + df_se, color="#3F5D7D")  

# Decorations
# Lighten borders
plt.gca().spines["top"].set_alpha(0)
plt.gca().spines["bottom"].set_alpha(1)
plt.gca().spines["right"].set_alpha(0)
plt.gca().spines["left"].set_alpha(1)
plt.xticks(x[::2], [str(d) for d in x[::2]] , fontsize=12)
plt.title("User Orders by Hour of Day (95% confidence)", fontsize=22)
plt.xlabel("Hour of Day")

s, e = plt.gca().get_xlim()
plt.xlim(s, e)

# Draw Horizontal Tick lines  
for y in range(8, 20, 2):    
    plt.hlines(y, xmin=s, xmax=e, colors='black', alpha=0.5, linestyles="--", lw=0.5)

plt.show()

"Data Source: https://www.kaggle.com/olistbr/brazilian-ecommerce#olist_orders_dataset.csv"
from dateutil.parser import parse
from scipy.stats import sem

# Import Data
df_raw = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/orders_45d.csv', 
                     parse_dates=['purchase_time', 'purchase_date'])

# Prepare Data: Daily Mean and SE Bands
df_mean = df_raw.groupby('purchase_date').quantity.mean()
df_se = df_raw.groupby('purchase_date').quantity.apply(sem).mul(1.96)

# Plot
plt.figure(figsize=(16,10), dpi= 80)
plt.ylabel("# Daily Orders", fontsize=16)  
x = [d.date().strftime('%Y-%m-%d') for d in df_mean.index]
plt.plot(x, df_mean, color="white", lw=2) 
plt.fill_between(x, df_mean - df_se, df_mean + df_se, color="#3F5D7D")  

# Decorations
# Lighten borders
plt.gca().spines["top"].set_alpha(0)
plt.gca().spines["bottom"].set_alpha(1)
plt.gca().spines["right"].set_alpha(0)
plt.gca().spines["left"].set_alpha(1)
plt.xticks(x[::6], [str(d) for d in x[::6]] , fontsize=12)
plt.title("Daily Order Quantity of Brazilian Retail with Error Bands (95% confidence)", fontsize=20)

# Axis limits
s, e = plt.gca().get_xlim()
plt.xlim(s, e-2)
plt.ylim(4, 10)

# Draw Horizontal Tick lines  
for y in range(5, 10, 1):    
    plt.hlines(y, xmin=s, xmax=e, colors='black', alpha=0.5, linestyles="--", lw=0.5)

plt.show()

参考资料

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