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 47.30% per annum.
- GOOG price at the close of May 7, 2024 was $172.98 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 30.01% per annum.
- GOOG price at the close of May 7, 2024 was higher than the top border of the secondary price channel by $4.45 (2.64%).
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 GOOG 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 26, 2022
End date: May 7, 2024
a = 3.1571
b = 0.0011
s = 0.0577
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 47.30%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0577) – 1
= 25.96%
October 26, 2022 calculations
Top border of price channel:
Exp(Y875)
= Exp(a + b × X875 + 2 × s)
= Exp(a + b × 1,267 + 2 × s)
= Exp(3.1571 + 0.0011 × 1,267 + 2 × 0.0577)
= Exp(4.6170)
= $101.19
Bottom border of price channel:
Exp(Y875)
= Exp(a + b × X875 – 2 × s)
= Exp(a + b × 1,267 – 2 × s)
= Exp(3.1571 + 0.0011 × 1,267 – 2 × 0.0577)
= Exp(4.3862)
= $80.34
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.1571 + 0.0011 × 1,826 + 2 × 0.0577)
= Exp(5.2102)
= $183.13
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.1571 + 0.0011 × 1,826 – 2 × 0.0577)
= Exp(4.9794)
= $145.39
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 47.30% per annum.
- GOOG price at the close of May 7, 2024 was $172.98 and was inside the primary price channel.
Secondary Trend
Start date: May 11, 2023
End date: May 7, 2024
a = 3.7353
b = 0.0007
s = 0.0395
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 30.01%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0395) – 1
= 17.10%
May 11, 2023 calculations
Top border of price channel:
Exp(Y1,010)
= Exp(a + b × X1,010 + 2 × s)
= Exp(a + b × 1,464 + 2 × s)
= Exp(3.7353 + 0.0007 × 1,464 + 2 × 0.0395)
= Exp(4.8669)
= $129.91
Bottom border of price channel:
Exp(Y1,010)
= Exp(a + b × X1,010 – 2 × s)
= Exp(a + b × 1,464 – 2 × s)
= Exp(3.7353 + 0.0007 × 1,464 – 2 × 0.0395)
= Exp(4.7090)
= $110.94
May 7, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.7353 + 0.0007 × 1,826 + 2 × 0.0395)
= Exp(5.1271)
= $168.53
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.7353 + 0.0007 × 1,826 – 2 × 0.0395)
= Exp(4.9693)
= $143.92
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 30.01% per annum.
- GOOG price at the close of May 7, 2024 was higher than the top border of the secondary price channel by $4.45 (2.64%).
- 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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