Spatio-Temporal Data Analysis - Week 1B: Time Series: Objects in Python and Visualization

Time Series

A time series is a sequence of observations taken sequentially in time.

Cross-sectional data

	ID	calories
0	1	420
1	2	380
2	3	390

Observations that come from different individuals or groups at a single point in time.

Time series data

	Year	Sales
0	2019	490
1	2020	980
2	2021	260

A set of observations, along with some information about what times those observations were recorded.

DateTime

Cross-sectional data

import pandas as pd
data = {
  "ID": [1, 2, 3],
  "calories": [420, 380, 390]
  
}

#load data into a DataFrame object:
dfc = pd.DataFrame(data)
dfc

	ID	calories
0	1	420
1	2	380
2	3	390

Time series data

data = {
  "Year": [2019, 2020, 2021],
  "Sales": [490, 980, 260]
  
}

#load data into a DataFrame object:
dft = pd.DataFrame(data)
dft

	Year	Sales
0	2019	490
1	2020	980
2	2021	260

DateTime

Cross-sectional data

dfc.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3 entries, 0 to 2
Data columns (total 2 columns):
 #   Column    Non-Null Count  Dtype
---  ------    --------------  -----
 0   ID        3 non-null      int64
 1   calories  3 non-null      int64
dtypes: int64(2)
memory usage: 176.0 bytes

Time series data

dft.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3 entries, 0 to 2
Data columns (total 2 columns):
 #   Column  Non-Null Count  Dtype
---  ------  --------------  -----
 0   Year    3 non-null      int64
 1   Sales   3 non-null      int64
dtypes: int64(2)
memory usage: 176.0 bytes

Necessary packages

import pandas as pd
import numpy as np
import datetime

Read AirPassenger

airpassenger = pd.read_csv('AirPassengers.csv')
airpassenger

	Month	#Passengers
0	1949-01	112
1	1949-02	118
2	1949-03	132
3	1949-04	129
4	1949-05	121
...	...	...
139	1960-08	606
140	1960-09	508
141	1960-10	461
142	1960-11	390
143	1960-12	432

144 rows × 2 columns

AirPassenger dataset

airpassenger.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 144 entries, 0 to 143
Data columns (total 2 columns):
 #   Column       Non-Null Count  Dtype 
---  ------       --------------  ----- 
 0   Month        144 non-null    object
 1   #Passengers  144 non-null    int64 
dtypes: int64(1), object(1)
memory usage: 2.4+ KB

Data Visualization

import plotnine
from plotnine import *
ggplot(airpassenger, aes(x='Month', y='#Passengers'))+geom_line()

<ggplot: (-9223372036479770161)>

Convert to Date and Time

from datetime import datetime
airpassenger['Month']= pd.to_datetime(airpassenger['Month'])
airpassenger.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 144 entries, 0 to 143
Data columns (total 2 columns):
 #   Column       Non-Null Count  Dtype         
---  ------       --------------  -----         
 0   Month        144 non-null    datetime64[ns]
 1   #Passengers  144 non-null    int64         
dtypes: datetime64[ns](1), int64(1)
memory usage: 2.4 KB

Data Visualization

ggplot(airpassenger, aes(x='Month', y='#Passengers'))+geom_line()

<ggplot: (-9223372036479774183)>

Data Visualization

ggplot(airpassenger, aes(x='Month', y='#Passengers'))+geom_line()+geom_point()

<ggplot: (-9223372036479770771)>

Split date into month and year

airpassenger['year'] = airpassenger['Month'].dt.year
airpassenger['month'] = airpassenger['Month'].dt.month

Split date into month and year (cont.)

airpassenger

	Month	#Passengers	year	month
0	1949-01-01	112	1949	1
1	1949-02-01	118	1949	2
2	1949-03-01	132	1949	3
3	1949-04-01	129	1949	4
4	1949-05-01	121	1949	5
...	...	...	...	...
139	1960-08-01	606	1960	8
140	1960-09-01	508	1960	9
141	1960-10-01	461	1960	10
142	1960-11-01	390	1960	11
143	1960-12-01	432	1960	12

144 rows × 4 columns

Time Series Patterns

Trend

Long-term increase or decrease in the data.

Seasonal

A seasonal pattern exists when a series is influenced by seasonal factors (e.g., the quarter of the year, the month, or day of the week). Seasonality is always of a fixed and known period. Hence, seasonal time series are sometimes called periodic time series.

Period is unchanging and associated with some aspect of the calendar.

Time Series Patterns (cont)

Cyclic

A cyclic pattern exists when data exhibit rises and falls that are not of fixed period. The duration of these fluctuations is usually of at least 2 years. In general,

the average length of cycles is longer than the length of a seasonal pattern.

the magnitude of cycles tends to be more variable than the magnitude of seasonal patterns

Example: trend

Example: seasonal

Example: multiple seasonality

Example: Trend + Seasonal

Cyclic

Cyclic + Seasonal

Frequency of a time series: Seasonal periods

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='year'))+geom_point()

<ggplot: (-9223372036478791978)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(year)'))+geom_point()

<ggplot: (-9223372036582484245)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(year)'))+geom_line()

<ggplot: (376120896)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(year)'))+geom_line() + geom_point()

<ggplot: (-9223372036479294681)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(month)'))+ geom_boxplot()

<ggplot: (-9223372036479434317)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(month)'))+ geom_point()+ geom_boxplot()

<ggplot: (-9223372036480369867)>

Seasonal plots

ggplot(airpassenger, aes(x='month', y='#Passengers', color='factor(month)'))+ geom_point()+ geom_boxplot(alpha=0.5)

<ggplot: (-9223372036477430072)>

Yearly variation

ggplot(airpassenger, aes(x='year', y='#Passengers', color='factor(year)'))+ geom_point()+ geom_boxplot(alpha=0.5)

<ggplot: (377342307)>