Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 98.11% per annum.
- GE price at the close of September 13, 2024 was $178.28 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 17.83% per annum.
- GE price at the close of September 13, 2024 was higher than the top border of the secondary price channel by $0.48 (0.27%).
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 GE 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: June 10, 2022
End date: September 13, 2024
a = 1.7903
b = 0.0019
s = 0.0870
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0019) – 1
= 98.11%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0870) – 1
= 41.63%
June 10, 2022 calculations
Top border of price channel:
Exp(Y690)
= Exp(a + b × X690 + 2 × s)
= Exp(a + b × 998 + 2 × s)
= Exp(1.7903 + 0.0019 × 998 + 2 × 0.0870)
= Exp(3.8336)
= $46.23
Bottom border of price channel:
Exp(Y690)
= Exp(a + b × X690 – 2 × s)
= Exp(a + b × 998 – 2 × s)
= Exp(1.7903 + 0.0019 × 998 – 2 × 0.0870)
= Exp(3.4855)
= $32.64
September 13, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(1.7903 + 0.0019 × 1,824 + 2 × 0.0870)
= Exp(5.3807)
= $217.17
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(1.7903 + 0.0019 × 1,824 – 2 × 0.0870)
= Exp(5.0326)
= $153.33
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 98.11% per annum.
- GE price at the close of September 13, 2024 was $178.28 and was inside the primary price channel.
Secondary Trend
Start date: April 5, 2024
End date: September 13, 2024
a = 4.3098
b = 0.0004
s = 0.0254
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 17.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0254) – 1
= 10.69%
April 5, 2024 calculations
Top border of price channel:
Exp(Y1,146)
= Exp(a + b × X1,146 + 2 × s)
= Exp(a + b × 1,663 + 2 × s)
= Exp(4.3098 + 0.0004 × 1,663 + 2 × 0.0254)
= Exp(5.1083)
= $165.38
Bottom border of price channel:
Exp(Y1,146)
= Exp(a + b × X1,146 – 2 × s)
= Exp(a + b × 1,663 – 2 × s)
= Exp(4.3098 + 0.0004 × 1,663 – 2 × 0.0254)
= Exp(5.0067)
= $149.41
September 13, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.3098 + 0.0004 × 1,824 + 2 × 0.0254)
= Exp(5.1806)
= $177.80
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.3098 + 0.0004 × 1,824 – 2 × 0.0254)
= Exp(5.0791)
= $160.62
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 17.83% per annum.
- GE price at the close of September 13, 2024 was higher than the top border of the secondary price channel by $0.48 (0.27%).
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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