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time series
1. Time series diagram
Time series graph is used to visualize how a given index changes with time. Here, you can learn how air passenger traffic changed between 1949 and 1969.
# 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()
2. Time series with markers
The following time series plots all peaks and troughs, and notes the occurrence of selected special events.
# 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()
3. Autocorrelation (ACF) and partial autocorrelation (PACF) graphs
The ACF chart shows the correlation between the time series and its own lag. Each vertical line (on the autocorrelation graph) represents the correlation between the sequence and the lag starting from lag 0. The blue shaded area in the image is the level of significance. Those above the blue line are huge lags.
So how to explain?
For air passengers, we see as many as 14 lags that have crossed the blue line, so it's significant. This means that the 14 year old air passenger volume has an impact on today's passenger volume.
On the other hand, PACF shows the autocorrelation between any given (Time Series) lag and the current series, but removes the lag between the two.
# 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()
4. Cross correlation graph
The cross correlation graph shows the time lag between two time series.
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()
5. Time series decomposition diagram
The decomposition diagram of time series shows the decomposition of time series by trend, season and residual components.
"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()
6. Multiple time series diagram
You can plot multiple time series measuring the same value on the same chart, as shown below.
"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()
7. Double y-axis graph
If you want to display two time series measuring two different quantities at the same time point, you can draw the second series again on the second Y-axis on the right.
"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()
8. Time series with error band
If you have a time series dataset with multiple observations at each time point (date / time stamp), you can build a time series with error bands. You can see some examples below based on orders placed at different times of the day. Another example is the number of orders that arrive in 45 days.
In this method, the average number of orders is represented by a white line. Then 95% confidence band is calculated and plotted around the mean.
"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()
"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()
9. Stacked area map
Stacked area map shows the contribution of multiple time series intuitively, so it can be easily compared with each other.
# Import Data df = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/nightvisitors.csv') # Decide Colors mycolors = ['tab:red', 'tab:blue', 'tab:green', 'tab:orange', 'tab:brown', 'tab:grey', 'tab:pink', 'tab:olive'] # Draw Plot and Annotate fig, ax = plt.subplots(1,1,figsize=(16, 9), dpi= 80) columns = df.columns[1:] labs = columns.values.tolist() # Prepare data x = df['yearmon'].values.tolist() y0 = df[columns[0]].values.tolist() y1 = df[columns[1]].values.tolist() y2 = df[columns[2]].values.tolist() y3 = df[columns[3]].values.tolist() y4 = df[columns[4]].values.tolist() y5 = df[columns[5]].values.tolist() y6 = df[columns[6]].values.tolist() y7 = df[columns[7]].values.tolist() y = np.vstack([y0, y2, y4, y6, y7, y5, y1, y3]) # Plot for each column labs = columns.values.tolist() ax = plt.gca() ax.stackplot(x, y, labels=labs, colors=mycolors, alpha=0.8) # Decorations ax.set_title('Night Visitors in Australian Regions', fontsize=18) ax.set(ylim=[0, 100000]) ax.legend(fontsize=10, ncol=4) plt.xticks(x[::5], fontsize=10, horizontalalignment='center') plt.yticks(np.arange(10000, 100000, 20000), fontsize=10) plt.xlim(x[0], x[-1]) # 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.show()
10. Area map (not stacked)
Unstacked area maps are used to visualize the progress (up and down) of two or more series relative to each other. In the chart below, you can see clearly how the personal saving rate will decrease as the median of unemployment increases. The unstacked area map shows this phenomenon well.
import matplotlib as mpl import calmap # Import Data df = pd.read_csv("https://raw.githubusercontent.com/selva86/datasets/master/yahoo.csv", parse_dates=['date']) df.set_index('date', inplace=True) # Plot plt.figure(figsize=(16,10), dpi= 80) calmap.calendarplot(df['2014']['VIX.Close'], fig_kws={'figsize': (16,10)}, yearlabel_kws={'color':'black', 'fontsize':14}, subplot_kws={'title':'Yahoo Stock Prices'}) plt.show()
11. Calendar heat map
Calendar map is an alternative to time series to visualize time-based data, rather than the preferred method. Although visually appealing, the values are not very obvious. However, it can effectively depict extreme values and holiday effects.
import matplotlib as mpl import calmap # Import Data df = pd.read_csv("https://raw.githubusercontent.com/selva86/datasets/master/yahoo.csv", parse_dates=['date']) df.set_index('date', inplace=True) # Plot plt.figure(figsize=(16,10), dpi= 80) calmap.calendarplot(df['2014']['VIX.Close'], fig_kws={'figsize': (16,10)}, yearlabel_kws={'color':'black', 'fontsize':14}, subplot_kws={'title':'Yahoo Stock Prices'}) plt.show()
12. Seasonal map
The seasonal chart can be used to compare the time series performance of the same day (year / month / week, etc.) of the previous season.
from dateutil.parser import parse # Import Data df = pd.read_csv('https://github.com/selva86/datasets/raw/master/AirPassengers.csv') # Prepare data df['year'] = [parse(d).year for d in df.date] df['month'] = [parse(d).strftime('%b') for d in df.date] years = df['year'].unique() # Draw Plot mycolors = ['tab:red', 'tab:blue', 'tab:green', 'tab:orange', 'tab:brown', 'tab:grey', 'tab:pink', 'tab:olive', 'deeppink', 'steelblue', 'firebrick', 'mediumseagreen'] plt.figure(figsize=(16,10), dpi= 80) for i, y in enumerate(years): plt.plot('month', 'traffic', data=df.loc[df.year==y, :], color=mycolors[i], label=y) plt.text(df.loc[df.year==y, :].shape[0]-.9, df.loc[df.year==y, 'traffic'][-1:].values[0], y, fontsize=12, color=mycolors[i]) # Decoration plt.ylim(50,750) plt.xlim(-0.3, 11) plt.ylabel('$Air Traffic$') plt.yticks(fontsize=12, alpha=.7) plt.title("Monthly Seasonal Plot: Air Passengers Traffic (1949 - 1969)", fontsize=22) plt.grid(axis='y', alpha=.3) # Remove borders plt.gca().spines["top"].set_alpha(0.0) plt.gca().spines["bottom"].set_alpha(0.5) plt.gca().spines["right"].set_alpha(0.0) plt.gca().spines["left"].set_alpha(0.5) # plt.legend(loc='upper right', ncol=2, fontsize=12) plt.show()
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