R Notebook

sample size

library(gtsummary)
library(dplyr)

##Major European Stock Indices, 1991–1998

head(EuStockMarkets)

Time Series:
Start = c(1991, 130) 
End = c(1991, 135) 
Frequency = 260 
             DAX    SMI    CAC   FTSE
1991.496 1628.75 1678.1 1772.8 2443.6
1991.500 1613.63 1688.5 1750.5 2460.2
1991.504 1606.51 1678.6 1718.0 2448.2
1991.508 1621.04 1684.1 1708.1 2470.4
1991.512 1618.16 1686.6 1723.1 2484.7
1991.515 1610.61 1671.6 1714.3 2466.8

DAX (Germany), SMI (Switzerland), CAC (France), FTSE (UK).

 data("EuStockMarkets")

summary(EuStockMarkets)

      DAX            SMI            CAC            FTSE     
 Min.   :1402   Min.   :1587   Min.   :1611   Min.   :2281  
 1st Qu.:1744   1st Qu.:2166   1st Qu.:1875   1st Qu.:2843  
 Median :2141   Median :2796   Median :1992   Median :3247  
 Mean   :2531   Mean   :3376   Mean   :2228   Mean   :3566  
 3rd Qu.:2722   3rd Qu.:3812   3rd Qu.:2274   3rd Qu.:3994  
 Max.   :6186   Max.   :8412   Max.   :4388   Max.   :6179  

  str(EuStockMarkets)

 Time-Series [1:1860, 1:4] from 1991 to 1999: 1629 1614 1607 1621 1618 ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"

 plot(EuStockMarkets)

Interpretation: 1. Structure of the Time Series

Your data is a multivariate time series (matrix time series with 4 variables). In R, when you use:

ts(data, start = c(1991, 130), end = c(1991, 135), frequency = 260)

1991.496, 1991.500, etc. → These decimal values are R’s way of expressing “year + fraction of the year”

1991.496 = 1991 + (130/260) ≈ mid-year (July).

1991.515 = 1991 + (135/260).

You have 6 daily observations (130th → 135th trading day).

So, R is placing your stock data along a trading-day calendar.

🔹 2. Market Movements in Your Data Day DAX (Germany) SMI (Switzerland) CAC (France) FTSE (UK) Start 1628.75 1678.1 1772.8 2443.6 End 1610.61 1671.6 1714.3 2466.8 Change ↓ -18.14 ↓ -6.5 ↓ -58.5 ↑ +23.2

DAX (Germany): Decreased → negative short-term movement.

SMI (Switzerland): Very stable, small decline.

CAC (France): Strongest decline, suggesting bearish pressure.

FTSE (UK): Only one showing an increase → relative market strength.

🔹 3. Possible Interpretation

This was likely a period where continental Europe (Germany, France, Switzerland) faced selling pressure, while UK market remained resilient.

This divergence might be due to:

Macroeconomic news (different economic conditions, monetary policy, or political events).

Currency differences (FTSE is GBP-denominated vs. others in continental currencies).

Sector composition (FTSE historically had strong oil/mining exposure, which may rise while others fall).

🔹 4. Statistical Analysis You Can Do in R

Here are some deeper analyses you might run:

1. Plot the series

plot.ts(your_timeseries, main=“European Stock Indices, 1991”, col=1:4)

This shows trends side by side.

2. Calculate daily returns (%)

returns <- diff(log(your_timeseries)) * 100

This gives percentage changes, which are better for comparison.

3. Correlation between indices

cor(returns, use=“complete.obs”)

This shows how closely the indices move together (usually high for European markets).

4. Summary statistics

summary(returns)

This gives min, max, mean, volatility.

🔹 5. Key Insights

Over 6 days, CAC dropped most (-3.3%), showing weakness in the French market.

FTSE gained (+0.9%), decoupling from others.

DAX and SMI fell slightly, consistent with mild bearishness.

Strong co-movement is expected, but here FTSE diverged → could indicate market-specific news.