Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 3.28% per annum.
- PEP price at the close of February 20, 2025 was $149.10 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 36.87% per annum.
- PEP price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $0.17 (0.11%). This indicates a possible reversal in the secondary trend direction.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PEP price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 24, 2022
End date: February 20, 2025
a = 5.2426
b = -0.0001
s = 0.0453
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -3.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0453) – 1
= 19.87%
October 24, 2022 calculations
Top border of price channel:
Exp(Y674)
= Exp(a + b × X674 + 2 × s)
= Exp(a + b × 976 + 2 × s)
= Exp(5.2426 + -0.0001 × 976 + 2 × 0.0453)
= Exp(5.2439)
= $189.42
Bottom border of price channel:
Exp(Y674)
= Exp(a + b × X674 – 2 × s)
= Exp(a + b × 976 – 2 × s)
= Exp(5.2426 + -0.0001 × 976 – 2 × 0.0453)
= Exp(5.0627)
= $158.02
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.2426 + -0.0001 × 1,826 + 2 × 0.0453)
= Exp(5.1662)
= $175.25
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.2426 + -0.0001 × 1,826 – 2 × 0.0453)
= Exp(4.9850)
= $146.20
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 3.28% per annum.
- PEP price at the close of February 20, 2025 was $149.10 and was inside the primary price channel.
Secondary Trend
Start date: September 3, 2024
End date: February 20, 2025
a = 7.2647
b = -0.0013
s = 0.0198
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -36.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0198) – 1
= 8.22%
September 3, 2024 calculations
Top border of price channel:
Exp(Y1,140)
= Exp(a + b × X1,140 + 2 × s)
= Exp(a + b × 1,656 + 2 × s)
= Exp(7.2647 + -0.0013 × 1,656 + 2 × 0.0198)
= Exp(5.2177)
= $184.51
Bottom border of price channel:
Exp(Y1,140)
= Exp(a + b × X1,140 – 2 × s)
= Exp(a + b × 1,656 – 2 × s)
= Exp(7.2647 + -0.0013 × 1,656 – 2 × 0.0198)
= Exp(5.1387)
= $170.49
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.2647 + -0.0013 × 1,826 + 2 × 0.0198)
= Exp(5.0035)
= $148.93
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.2647 + -0.0013 × 1,826 – 2 × 0.0198)
= Exp(4.9245)
= $137.62
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 36.87% per annum.
- PEP price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $0.17 (0.11%). This indicates a possible reversal in the secondary trend direction.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
Check out PEP and 1,499 other stocks on our new website