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 115.46% per annum.
- PG price at the close of May 17, 2024 was $167.64 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 73.85% per annum.
- PG price at the close of May 17, 2024 was inside the secondary price channel.
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 PG 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: April 3, 2024
End date: May 17, 2024
a = 1.2897
b = 0.0021
s = 0.0083
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 115.46%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0083) – 1
= 3.36%
April 3, 2024 calculations
Top border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 + 2 × s)
= Exp(a + b × 1,780 + 2 × s)
= Exp(1.2897 + 0.0021 × 1,780 + 2 × 0.0083)
= Exp(5.0496)
= $155.96
Bottom border of price channel:
Exp(Y1,226)
= Exp(a + b × X1,226 – 2 × s)
= Exp(a + b × 1,780 – 2 × s)
= Exp(1.2897 + 0.0021 × 1,780 – 2 × 0.0083)
= Exp(5.0166)
= $150.90
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(1.2897 + 0.0021 × 1,824 + 2 × 0.0083)
= Exp(5.1422)
= $171.08
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(1.2897 + 0.0021 × 1,824 – 2 × 0.0083)
= Exp(5.1091)
= $165.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 115.46% per annum.
- PG price at the close of May 17, 2024 was $167.64 and was inside the primary price channel.
Secondary Trend
Start date: April 23, 2024
End date: May 17, 2024
a = 2.3573
b = 0.0015
s = 0.0042
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 73.85%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0042) – 1
= 1.71%
April 23, 2024 calculations
Top border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 + 2 × s)
= Exp(a + b × 1,800 + 2 × s)
= Exp(2.3573 + 0.0015 × 1,800 + 2 × 0.0042)
= Exp(5.0931)
= $162.90
Bottom border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 – 2 × s)
= Exp(a + b × 1,800 – 2 × s)
= Exp(2.3573 + 0.0015 × 1,800 – 2 × 0.0042)
= Exp(5.0762)
= $160.17
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.3573 + 0.0015 × 1,824 + 2 × 0.0042)
= Exp(5.1295)
= $168.93
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.3573 + 0.0015 × 1,824 – 2 × 0.0042)
= Exp(5.1126)
= $166.10
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 73.85% per annum.
- PG price at the close of May 17, 2024 was inside the secondary price channel.
- 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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