📖 数据类型：截面、时间序列、面板

                   ┌─────────────────────┐
                   │ 数据集中有几个个体？  │
                   └─────────┬───────────┘
                             │
              ┌──────────────┼──────────────┐
              ↓              ↓              ↓
          「1 个」        「多个」        「多个」
                             │              │
                    ┌────────┴────────┐     │
                    ↓                 ↓     ↓
               「1 个时间点」    「多个时间点」
                    ↓                 ↓
               「截面数据」      「面板数据」

📌 Topic: Understanding the Three Fundamental Data Structures — Where Quantitative Analysis Begins

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1. Why Do Data Types Matter?

In CFA Level 1 Quantitative Methods, data is the raw material. The analytical tools you use depend first and foremost on what type of data you are dealing with.

Scenario	What Type of Data?
Comparing P/E ratios of all S&P 500 constituents as of year-end 2025	Cross-Sectional
Examining Moutai's stock price trend over the past 5 years	Time Series
Analyzing ROE changes across 50 stocks over 10 years simultaneously	Panel

💡 Identifying data types is the first foundational skill in CFA Level 1 Quant. Exam questions won't ask for definitions directly — they will describe a scenario and expect you to classify the data. So learn through examples, not by rote memorization.

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2. The Three Data Types Explained

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2.1 Cross-Sectional Data

Definition: Data collected by observing many subjects at the same point in time.

Keywords: Same time + Different individuals

Key Characteristics

Feature	Description
Time Dimension	Fixed (one point or period)
Individual Dimension	Multiple (companies, people, countries, etc.)
Typical Use	Comparison, ranking, cross-sectional regression
Analytical Tools	Mean, variance, quantiles, scatter plots, cross-sectional regression

Real-World Examples

Example 1: Corporate Financial Comparison

On December 31, 2025, gather ROE, debt-to-asset ratio, and P/E ratio for all CSI 300 constituent stocks.

Company	ROE	Debt/Asset	P/E
Kweichow Moutai	32.1%	18.5%	28.3
CATL	18.7%	52.3%	35.6
...	...	...	...
300 rows total

🎯 This is cross-sectional data: one point in time (12/31/2025), 300 individuals (companies), 3 variables.

Example 2: Fund Manager Performance Ranking

Annualized returns for 500 equity funds for the 2025 fiscal year — same period, different funds (individuals).

Example 3: Consumer Survey

A survey conducted in June 2025 collects data from 1,000 respondents on their willingness to purchase a financial product, along with age and income — same time period, different individuals.

Key Pitfall of Cross-Sectional Data

⚠️ Cross-sectional data cannot capture "change" — you can see which company has the highest ROE at a given moment, but you cannot see how one company's ROE changed year by year. For that, you need time series data.

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2.2 Time Series Data

Definition: Data collected by observing the same subject across multiple points in time.

Keywords: Same individual + Different times

Key Characteristics

Feature	Description
Time Dimension	Multiple (daily/monthly/quarterly/annual)
Individual Dimension	Fixed (one)
Typical Use	Trend analysis, forecasting, seasonal adjustment
Analytical Tools	Moving average, autocorrelation, ARIMA, trend lines

Real-World Examples

Example 1: Moutai Stock Price

Kweichow Moutai monthly closing price from January 2021 to December 2025:

Time	Closing Price (CNY)
2021-01	2,050
2021-02	2,100
2021-03	2,030
...	...
2025-12	1,820

🎯 Same individual (Moutai), 60 time points (60 months), 1 variable (stock price) → Time series.

Example 2: China GDP Growth

China's annual GDP growth rate from 2000 to 2025 — same economy, 26 years.

Example 3: Portfolio Returns

Daily returns of your investment portfolio for each trading day in 2024 — same portfolio, approximately 250 trading days.

Unique Challenges of Time Series Data

Issue	Description
Autocorrelation	Today's value correlates with yesterday's — observations are NOT independent; ordinary regression cannot be used directly
Trend	Data may trend upward or downward over the long term
Seasonality	Retail Q4 revenue is highest — patterns that repeat annually
Structural Break	Policy changes or financial crises → the "pattern" of the data changes

🎯 Later chapters in CFA Level 1 Quant will dive deeper into these time series properties. For now, remember: time series ≠ cross-sectional data, because observations have sequence and dependency.

Time Series vs. Cross-Sectional Data at a Glance

Dimension	Cross-Sectional	Time Series
Number of Individuals	Many (N)	1
Number of Time Points	1	Many (T)
Data Table Shape	N rows × 1 column (per variable)	T rows × 1 column
Source of Variation	Across individuals	Across time
Analytical Goal	Comparison/Ranking	Trend/Forecasting
Independence Assumption	Usually assumed independent	Not independent (autocorrelation)

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2.3 Panel Data

Definition: Data collected by observing multiple individuals across multiple points in time.

Keywords: Multiple individuals + Multiple times

Panel data = Cross-sectional data + Time series data combined.

Key Characteristics

Feature	Description
Time Dimension	Multiple
Individual Dimension	Multiple
Typical Use	Panel regression, fixed effects, random effects
Analytical Tools	Panel regression (CFA Level 1 does not require deep calculation, but you must recognize it)

Real-World Examples

Example 1: CSI 300 Financial Data Over 5 Years

Company	Year	ROE	Debt/Asset	Market Cap
Moutai	2021	31.2%	20.1%	280B
Moutai	2022	30.8%	19.3%	265B
Moutai	2023	31.8%	18.7%	310B
Moutai	2024	32.4%	18.2%	305B
Moutai	2025	32.1%	18.5%	320B
CATL	2021	15.2%	55.0%	...
...	...	...	...	...

🎯 300 companies × 5 years = 1,500 rows. You can see both how each company changes over time AND how companies differ from one another in each year.

Example 2: Major Economies Over 20 Years

Country	Year	GDP Growth	CPI
China	2005	11.3%	1.8%
China	2006	12.7%	1.5%
...	...	...	...
USA	2005	3.5%	3.4%
USA	2006	2.9%	3.2%
...	...	...	...

🎯 This table contains 2 dimensions simultaneously: cross-section (country comparison) + time (annual trend).

Example 3: Monthly NAV of 50 Funds

50 funds × 36 months = 1,800 observations. You can analyze both "performance trends of each fund" and "performance differences across funds."

Unique Advantages of Panel Data

Advantage	Description
Controls for individual heterogeneity	Separates "firm-specific characteristics" from "time trend" effects
More information	N × T observations, greater degrees of freedom
Studies both change and difference	Cross-section only captures differences; time series only captures changes; panel captures both

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3. Quick Identification Framework

Identification Decision Tree

                   ┌──────────────────────────┐
                   │ How many individuals/subjects? │
                   └────────────┬─────────────┘
                                │
              ┌─────────────────┼──────────────────┐
              ↓                 ↓                  ↓
          "1"              "Multiple"           "Multiple"
                                │                  │
                    ┌───────────┴───────┐          │
                    ↓                   ↓          ↓
              "1 time point"    "Multiple time points"
                    ↓                   ↓
            "Cross-Sectional"      "Panel"

Quick Mnemonic:

Mnemonic	Data Type
"Same moment, compare across"	Cross-Sectional
"Same subject, look over time"	Time Series
"Both across and over time — a big table"	Panel

Quick Classification Drill

Description	Data Type
Market cap of all A-share stocks on June 30, 2025	Cross-Sectional ✓
Daily closing level of the Shanghai Composite Index, 2010–2025	Time Series ✓
Quarterly ROE of 500 companies over 10 years	Panel ✓
Your personal account balance at month-end for the past 3 years	Time Series ✓
Today's fund size ranking across the entire market	Cross-Sectional ✓
Average wage across 30 industries over 5 years	Panel ✓
Yield-to-maturity of the same bond over the past 5 years	Time Series ✓

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4. Data Types and CFA Level 1 Topic Areas

Topic Area	Data Type Involved	Typical Exam Question
Descriptive Statistics	Primarily cross-sectional	Given a dataset, compute mean, median, standard deviation
Probability & Distributions	Cross-sectional	Assume returns follow a normal distribution
Sampling & Estimation	Cross-sectional	Infer population parameters from a cross-sectional sample
Hypothesis Testing	Cross-sectional	Test for differences in means between two groups
Simple Linear Regression	Cross-sectional	Use ROE to explain P/E, sample is cross-sectional
Technical Analysis (Equity)	Time Series	Moving averages, trend analysis
Time Series Analysis (Level 2)	Time Series	Autocorrelation, cointegration (not tested at Level 1, but data type must be known)
Ratio Analysis (FSA)	Cross-Sectional + Time Series	Multi-year trend for the same company + peer comparison

🎯 CFA Level 1 is predominantly cross-sectional analysis. Time series appears in technical analysis and some economic indicators. Panel data appears only for identification — panel regression calculations are not tested.

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5. Common Mistakes and Exam Traps

Trap 1: Mistaking "multiple individuals over a time period" for time series

❌ Wrong: "ROE of all CSI 300 companies from 2020–2025" — This is panel data, not time series!

Time series = one individual, multiple time points. Here there are multiple individuals.

Trap 2: Mistaking "multiple metrics at one time point" for panel data

❌ Wrong: "Moutai's ROE, debt-to-asset ratio, gross margin, and net margin in 2025" — This is cross-sectional data!

Multiple variables ≠ multiple time points. Still the same time, same individual — just measuring multiple variables.

Trap 3: Confusing data frequency with data type

❌ Wrong: Thinking "daily data = time series."

Data frequency (daily/monthly/quarterly/annual) is unrelated to data type. Daily quotes can be cross-sectional (all stocks' quotes today) or time series (one stock's quotes over 250 days).

Trap 4: Stacked cross-sections ≠ panel data

❌ Wrong: Pasting two years of cross-sectional data together counts as panel data.

✅ Correct: It must be the same group of individuals observed repeatedly across time to count as panel data. If the S&P 500 constituents in 2024 and 2025 differ (companies enter and exit), it is not strictly a balanced panel.

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6. How CFA Exam Questions Are Framed

CFA Level 1 will not ask directly "Which of the following is cross-sectional/time series/panel data?" but it will embed data type cues in the scenario. You need to:

1. Identify the data structure → determine which analytical method to use
2. Assess independence of observations → cross-sectional usually assumes independence; time series does not
3. Distinguish sources of variation → "differences across individuals" vs. "changes over time"

Exam-Style Examples

Example 1:

An analyst collects earnings per share (EPS) and P/E ratio data for all S&P 500 constituents in 2025. The analyst wants to study whether EPS correlates with P/E. What type of data is this?

A. Time series data B. Cross-sectional data C. Panel data

Answer: B → Same point in time (2025), multiple companies (500), so this is cross-sectional data.

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Example 2:

A fund manager records the monthly returns of his 3 managed funds over the past 60 months. He wants to compare risk-adjusted returns across the 3 funds. The data structure is:

A. Time series data B. Cross-sectional data C. Panel data

Answer: C → 3 individuals (3 funds) × 60 time points = panel data.

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Example 3:

An analyst collects annual free cash flow data for a single company from 2018 to 2025 for the purpose of forecasting future trends. This data is:

A. Cross-sectional data B. Time series data C. Panel data

Answer: B → Same company, multiple years, so this is time series.

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7. Practice Questions (5 Questions)

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Question 1

An analyst collects the following data: dividend yields of all Hang Seng Index constituents as of December 31, 2024. This data is:

A. Time series data B. Cross-sectional data C. Panel data

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Question 2

Which of the following is most likely to require panel data analysis?

A. Comparing the average ROE of the technology sector versus the financial sector in 2024 B. Analyzing the revenue growth trend of the same company over the past 10 years C. Studying the relationship between R&D expenditure and revenue growth for 200 listed companies over the most recent 5 years

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Question 3

Regarding the difference between time series data and cross-sectional data, which statement is correct?

A. Observations in time series data are generally considered mutually independent B. Cross-sectional data contains observations of the same individual at multiple time points C. Adjacent observations in time series data may exhibit autocorrelation

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Question 4

An analyst is studying "the relationship between GDP growth and fixed asset investment growth across 30 provinces over the past 15 years." How many observations does the dataset contain? (Assume no missing values)

A. 30 B. 15 C. 450

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Question 5

Which of the following datasets is NOT cross-sectional data?

A. Net profit reported by all A-share listed companies in a given fiscal year B. Daily net asset value (NAV) of a particular ETF over the past year C. Risk preference scores of 500 respondents from an investor survey

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8. Answers and Explanations

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Question 1 — Answer: B (Cross-sectional data)

Explanation: Same point in time (12/31/2024), multiple individuals (all Hang Seng Index constituents), one variable (dividend yield).

• ❌ A: Only one time point, not time series
• ✅ B: Meets the definition of cross-sectional data — same time, multiple individuals
• ❌ C: Only one time point, not panel

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Question 2 — Answer: C

Explanation:

• A: Same time point, multiple sectors → cross-sectional data; panel not needed
• B: One company, multiple years → time series; panel not needed
• C ✅: 200 companies (multiple individuals) × 5 years (multiple time points) → panel data

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Question 3 — Answer: C

Explanation:

• ❌ A: Observations in time series typically exhibit autocorrelation (today correlates with yesterday); they are NOT independent
• ❌ B: This is the definition of time series, not cross-sectional
• ✅ C: Correct. Adjacent time series observations are often correlated — this is a core characteristic of time series data

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Question 4 — Answer: C (450)

Explanation:

30 provinces × 15 years = 450 observations (assuming complete data for every province-year).

• ❌ A (30): Only counted the provinces, ignoring years
• ❌ B (15): Only counted the years, ignoring provinces
• ✅ C: Panel data observation count = N × T = 30 × 15 = 450

🎯 Common CFA Level 1 trap: describing "multiple individuals × multiple time periods" and asking you to calculate the number of observations. Formula: N × T.

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Question 5 — Answer: B

Explanation:

• A ✓ Cross-sectional: Same time (one fiscal year), multiple companies, net profit
• B ✗ NOT cross-sectional: One ETF, multiple time points (each trading day) → This is time series data
• C ✓ Cross-sectional: Same survey wave, 500 respondents, risk preference scores

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9. Section Summary

Data Type	Individuals	Time Points	Key Feature	CFA Level 1 Role
Cross-Sectional	Many	1	Compare across, same moment	Most common (stats, regression)
Time Series	1	Many	Track one subject, look over time	Technical analysis, economic indicators
Panel	Many	Many	Both dimensions, most comprehensive	Identification only, no calculation tested

Three-Step Identification Method

1. Check individuals: 1 or many?
2. Check time: 1 or many?
3. Cross-reference:
4. Many individuals + 1 time = Cross-Sectional
5. 1 individual + Many times = Time Series
6. Many individuals + Many times = Panel

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10. Next Lesson Preview

L100 Parameter vs. Statistic — The true value of a population is a parameter; the estimate from a sample is a statistic. This is the critical bridge from "describing data" to "statistical inference." Get ready to distinguish μ and x̄!

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📊 Core Credo: Data is the eyes of analysis. Choosing the wrong data type = using the wrong analytical method. Cross-sectional compares across, time series looks over time, panel captures both. Identifying data types is the first foundational step in CFA Level 1 Quant.